No, they cannot learn any move through breeding, although they can learn some. There are specific "egg moves" that each pokemon can learn if a female of the pokemon you want is bred with a male who knows the move and is in the same egg group. If you go to the move's page, if it can be bred then scroll down and there will be an "egg moves" section telling you which pokemon can learn the move through breeding. You also can go to a pokemon's page and look at the egg moves section to see what moves it can learn through breeding. As you'll see on Infernape's page http://pokemondb.net/pokedex/infernape , the egg moves that he can learn (as of b/w) are Assist, Blaze Kick, Counter, Double Kick, Encore, Fake Out, Fire Punch, Focus Energy, Focus Punch, Heat Wave, Helping Hand, Quick Guard, Submission, and Thunderpunch. So no, it can not learn blue flame.
Also, by blue flame do you mean blue flare? The only pokemon that can learn blue flare is Reshiram. Obviously, Reshiram does not breed, so no other pokemon can learn it even through breeding.