Okay, there are quite a few theories, but here are the major ones I know. (And the probably of their truth)
BHK is Sora's brother: The one explained here, Chance of being real: 0-5% (Extremely doubtful)
BHK is sora's shell: A theory where BHK is sora's shell, possible, but doesn't seem right since sora still has his heart. Chance of being real: 0-50%? (Not sure, but it makes sense)
BHK has lost his memories: A theory I came up with, BHK (just as sora) lost his memories due to namine, however, he did not get them back. And somehow they were gone forever, and all he can remember is a few blips (Such as twilight town, and probably sora). And since there's the theory that all of the keyblade wielders are connected, that explains it. i've got a bit more, but I won't post it, I have it in the BHK offical topic reborn, i'll either re-post it again, or just put it somewhere. Anyways, chance of being real, 0-50%? (Seems most likely to me)