Oh my gosh! That was totally me as a little kid. Not with all animals, but ALL dogs, big or small. I am not sure why it happened either, I do remember screaming and running away after being chased by the neighbor's dog once, but I think I was already afraid of them at that point. Unfortunately, I don't have much advice, though. I would start small, and let him observe from a distance he feels safe at. Don't make hom go around big, hyper dogs. From my experiences, I would think your basenji would actually be a good choice to start, because they are generally quiet and while spunky, don't slobber all over you, or come running at you like they are going to kill you!
It might just be something he has to grow out of…I am still not out of it yet...I love Tosca, but wasn't crazy about dogs at all until we got her (my husbands' begging). Since then I have opened up completely to her ( I think I like Tosca more than he does now, lol) and other small dogs are ok, but I still strongly dislike big dogs that come bounding up to you, jumping on you, barking loudly at you, and slobbering all over you.
When we are walking, if a big dog is unleashed and comes running out at us, I still freak out...not only for Tosca's sake, but I get scared too, I am short, and this thing could be viscious and plow me over, you never know!!!
So it might just be a part of his personality...however, with slow exposures that he is comfortable with (Whatever you do, DON"T FORCE it) hopefully he can become tolerable around dogs, at least small ones and other animals. He may never be an animal lover though 
LOL, when everyone still says to me "YOU got a dog?!?" I always say, "Tosca is not a dog, she is too weird and cute to be a dog...she is just my pet."
I would try to find a good book about all kind of animals which is written for kids. This explains how dogs, cats and other animals behave and what their reactions on some behaviour might be. Then I would try to find nice and patient, friendly animals and introduce them to him. But slowly. Does he go to a kindergarden? Maybe his mother should talk to them about these problems. In a group kids often can overcome such problems.
But never put pressure on him, which will increase the problems for sure.
Good luck!
Esther
My sister was like that as a kid too…..absolutely terrified of dogs, after someone had their 2 boxers off leash at the beach, which would be fine with the right owner and the right dogs, but they jumped on her and put her on the ground.
But, she definitely grew out of it, and now has this HUGE mutt that she loves more than anything.
His father definitely thinks "we should just get a dog, then he will get used to them" but I think that might be a little too forceful. He isn't in kindergarten yet, but I think he starts in the fall. I will mention that might help.
Thanks for the tips!
If your bil does decide to get a dog so he'll "get over it", for Heaven's sake tell him to NOT GET A PUPPY!!!
Puppies can be the WORST thing for helping a fearful kid get over their fears of dogs – crazy activity, razor sharp teeth, etc. all freak those kids out something fierce!
A calm, adult dog trained to sit,stay,down, etc would be the best way to go...if they must go that way.
I think the boy may benefit from visiting people who have dogs that are indifferent to kids; the dogs that tolerate, but would rather ignore them.
Then he will see that he can be around dogs, but the dogs aren't necessarily around him.
They may be looking at a long process though. I hope his dad is patient.
I think Amber (Logan's mom, my Sister in law) will make sure that they don't just get a dog….that is a little too forceful for Logan, but I will mention to her about puppies- you are right about their activity level is waaaay too high for him.
I think there is an older lab in one of their families that is exactly what you describe....indifferent to the kids, tolerant, but would rather ignore them.
Jack is too anxious to try and help. He loves kids, and will sit for them and let them tug on his ear, and touch his face, so he always goes too close for Logan's comfort.
I know of dogs and other animals used as therapy assistants. Maybe this direction could be a good idea. They are trained to stay calm and usually they can only educate the coolest and calmest of them to become Therapy-dog or cat or whatever….
Esther
I was bitten three different times as a child, and one of those incidents put me in the hospital for an evening to get stitches. To say I had a fear of dogs is putting it mildly. I didn't like them, I didn't trust them, breed be darned. If the 38-year old me could go back and tell the 8-year old me that one day I'd own a dog and love it to death, I would never believe me.
Take it slow with the kid, and explain the psychology of dogs. Let him know the sniffing thing is just the dog learning your "name". Show him how dogs respond to your emotions. Most importantly, don't rush him…he'll figure it out at his own pace. Trust me...if I can become a dog owner, anybody can.
I used to do animal theropy with disabled people with my lab, if you can find a dog that is that well trained and remains calm no matter what, and also maybe plays fetch so your nephew doesn't have to get up close and personal right off the get go. My friend is terrified of large dogs, and I had her play fetch with Hershey(my lab). She was very jumpy when Hershey ran back at her with the frisbee until she saw the dog stopped quiet a ways from her. My friend now lives in a house with a very large husky.
I think its interesting that the child is afraid of all animals not just dogs (so it's not just a case of some neighbor dog frightened him). My two cents would be just what annyaa suggested - contact a therapy dog person to have him/her introduce your nephew to the most calmest animal. Keeping all animals away from your nephew is definitely not the way to go (unless he has an allergy to all animals -but I don't believe that is possible).
Our Buana is a service dog for children that are afraid of dogs,
The most important thing (what a lot of people already said) is to stay calm, also the dog may not become nervous.
You can try to let your sister in law, stay with your B (if you can trust him enough to help your little nephew) and sit with him, maybe on the leash, and you stay with your nephew as far away as he's comfortable.
His mom will be the most important person on the planet, so he will react sooner when she has the dog.
Just let him look at his mom, maybe after a little while (maybe the first time after a few minuts, but maybe even after a few times trying) he will come closer, a few steps.
If you repeat that so often he will be feeling normal and eventually comes closer every time. (don't be scared if he have a bad day)
Look very closely at the behavoir of the child and the dog, and also the behavior between those two.
Your B, needs enough time to stay calm and still, and it cost some time.
You can observe your nephew and most of the time he decide by himselfe how close he get.
Fear is so complicated and needs so much time and cost a lot of energy from everyone.
Don't push it, that's only making it worse.
If he's comfortable enough, try at the end of a session to move a bit with the dog, walk a few steps, let him "do" someting small, so your nephew will learn that also some movement is not scary.
You can make the time longer, the movements bigger, etc.
Just let them look at eachoter, very very much. and hopefully he'll learn to come closer.
Maybe even in a while you ca start with petting him (as example on his back, away from his head, children mostly are afraid of the head)
Good luck! let us know how it will go with your little nephew
My son has been afraid of animals his entire life. We didn't know it until we were visiting a friend when he was 1 year old and their cat WALKED across the room. He freaked out. From that point on he was afraid of any live animal, but loved stuffed animals. He is 6 now and we just got an 8 week old Basenji. We talked about it alot, (he has slowly gotten used to our friend's cat, but every time the animal made a sudden move he jolted). He was excited to get the puppy, and we sat with him while he got used to exactly what the puppy would do. It has only been 2 months and my son is so good with our dog that he is not afraid of the dogs across the street who are high strung little fluffy things that always sent him runnning and screaming into the house. When I asked him about it he said he wasn't afraid now because he had one now. We waited to get a dog until both of our kids were older and could handle some responsibility. It was the best decision we made. He is still uncomforable around large dogs and other large animals, but has made remarkable progress. I don't know how your nephew will respond, but as he gets older he may realize that he has some control over the animals and that may help. Good luck!!!
