25 years ago I had a similar problem with our first basenji. It ended up the vet I was using at the time took a 'plug,' I think it's like a scraping but he gets more to test. He sent it somewhere to be evaluated.
In the meantime, I changed her food. At the time, around here, if you wanted to buy dog food, you got it at the grocery store. So after the skin issue, I bought Nutros at a more 'farm and feed' store. Before the results came back, her skin was clear, I think maybe a week and a half. My dogs have eaten Nutros since and I have had no skin problems. The result of the skin test they said was plants, and listed them - can't remember wht they said. One was grass. Hmmm, changing her food took care of the problem???
The VERY FIRST thing to address is your puppy's flea problem. I have no advice to offer, but know that is most important. The only time I have seen one or 2 fleas on them is when they catch, and eat, a rabbit. So, I get rid of the flea, go out and look for what's left of the rabbit, and watch for tapes.
The following is technically not about basenjis, so it's ok to skip it:
I'm going to share my way of thinking when it comes to health problems with my dogs, my kids, and my garden (I have a very extensive ornamental 1 acre garden - one time I heard people said "The dog and flower lady lives there")
1 When my dogs had a skin problem, first I looked at what's going IN the body - it has never been what ever is gotten when a flea bites them. So, I changed the food, there's so much in the dog food that anything can be causing the problem. Admittedly, I have been very lucky in regards to my dog's health.
2 When my son was little, he started complaining his leg hurt. I took them to a DO, because though they have the same training as an MD, they also have some training in the stuff a chiropractor does, and they seem to look at the whole body. The doctor we saw, my usual was on vacation, sent us to orthopedic guy, but not a Pediatric orthopedic guy.
That dr took an xray, showed it me, and pointed out where it showed my son had Legg Perthes (hip problem) He wore a weird brace for over a year, and we saw my usual dr. He sent us to a pediatric ortho guy, who took an xray. No problem seen, no more brace because NO LEGG PERTHES (Legg Perthes is not something that just cures itself!) We went back and saw my DO, he looked at my son for 2 minutes, and said "That little boy has FLAT FEET!!!! We got really good shoes, the problem was gone!
3 In my garden, my philosophy is feed the soil, let it feed the plants. I never use purchased fertilizer, but chop up any spent flowers (I go around and 'dead head' my flowers) that chop off, and garden debris that would not cause problems, and in the fall, I mow the yard with it's leaves from many many oak trees, and blow them into the side of our yard. The side of the yard is all fenced in, all planted with ornamentals - free fertilizer in my mind. In the fall I buy a few bags of alfalfa meal, and spread it. Alfalfa is a crop that framers plant to rejuvenate their soil. Since it grows with roots that go down 20' it brings up whatever nutrients are in the soil, then the farmer just plows it under. So, I use those nutrients that the roots bring up, as fertilizer.
No chemicals used, only cost is the gas for John, Deere!