If the second punch is always coming after the first (as apposed to being the other punch button) you should start it from the recovery frames on the first punch, and have it interrupt them (preferably interrupt them at a specific frame) otherwise he is going to throw a punch, reposition his body back into his standing stance, then throw another punch, as apposed to punching twice in a row, where the second punch usually starts before you have moved all the way back into stance, or depending on the style, without moving back into stance at all. It also might be kinda neat if you had a version of the recovery frame(s) where he was cambering the second punch that was the start of the second, and interrupted the first animation a little earlier. I dun really know what you are coding/making this in tho, and what kind of limitations it has. If interrupting animations is a no go, I would break the first punch into two animations, one punching and one recovering, and then if the player has hit attack again before the recovery animation started, he throws the second one, otherwise he plays the recovery animation, and cant attack again for a fraction of a second.
Just food for thought, mostly, and not proper critique, but thinking about it that way may help with the second punch animation.