Hi! I think to determine the best relaxer for you, we need to know the STRENGTH of your hair as well as the texture. Is your hair coarse, fine, or medium textured? Does it resist relaxing? Is it really dry in its natural state, or not so much? I think these are the things that matter more than just the kinkiness of your hair. My hair is VERY kinky, too, as in when it is natural it curls up onto itself into a single O, no waves or defined curls in sight!
However, the diameters of my individual hairs are small, which I now know means my hair is fine and that is why it can't take as much heat or strong relaxers that others do fine with. I also have very dry hair naturally, even in comparison with other 4a's and 4b's, so I know I need a LYE perm rather than a No-LYE... If you are unsure of the texture of your hair, you can go to growafrohairlong.com to see visual examples, among other sites.
Also, I read this on this board about relaxers and it stuck with me -- relaxers are called relaxers and not straighteners because all the chemical does is RELAX your hair bonds to "unlock" your curl pattern -- but it is YOU/YOUR STYLIST who is the actual "straightener," with her combing and smoothing motions. So besides finding a good perm, maybe you should also perfect your smoothing technique if you are self relaxing -- that should help you get straighter results.
By the way, people on this site seem to rave about Mizani, Designer's Touch and Designer's Essentials, Elucence (known to be gentle), Creme of Nature LYE (not the box one, which is No-LYE), and PHYTO, which is EXPENSIVE but good -- I've used it)
I hope I have helped! Here's wishing you the BEST of luck on your search!!!