It is always a bit dicey to convince 2 dogs to get along after blood has been shed. When my 2 boys were intact, fall was ALWAYS worse and I wouldn't even let them look at each other too long. They have been in several fights, but I always managed to gain a somewhat peacable household after a fight, but it was a slow process and I never leave them out together when I'm not home. (Even today when they are almost 14 and 15 years old. Digital is loose and Jet is in an expen.) I don't have any delusions that I was able to get them reintroduced b/c I'm a wonderful dogmom, I think I just got lucky. If you really want to keep both, you may have to run 2 separate packs forever. I don't think anyone can really say for sure. Running 2 separate packs is doable, especially in an adult-only home, but it does take dedication. You just need to figure out if you're willing to do that or not.
For right now, I'd keep the boys separated. IMO, if you can keep one in an expen with the other in the same room peacable, there's some hope. I'd also brush up on the obedience, mat work (google Overall's Relaxation Protocal), get a DAP. You want to make sure everyone is exercised (esp the high-on-hormones intact male basenji). Do you have someone else that can walk Flame while you walk Tucker? I think this would be great to do if you could walk them about 10-12 feet apart but parallel, depending on each dog's comfort zone. You just want to kiss on that comfort zone, not push into it too hard if that makes sense.
Personally, I don't hold much faith in the "support one as dominant, feed/pet/play with that one first, etc", but that sort of advice is out there.
I would look into different methods of getting 2 dogs to get along and figure out what feels right to you. Then look for a good behaviorist/trainer to help.
Literature about dog-dog issues, just off the top of my head:
William Campbell (i really liked his "happy dance routine", but I can't remember which book I read about it in. Here's one of his books from dogwise. Looks good, I should get it and read/reread it) http://www.dogwise.com/itemdetails.cfm?ID=DTB101
McConnell's Feeling Outnumbered - this is a booklet, not a full book. There is a little about 2 dogs who don't get along, but it's more a comprehensive look at living with dogs. For the price, i think it's a good deal.