If Cap makes a close combat attack and KO's an oponent while BAB is used for the +2 does followthrough still take effect.

How does the timing work for this?

I would say you cannot use Followthrough and still get the bonus for BAB. Since you're technically using a power in close combat, you would not qualify for BAB, which states:

Since Followthrough is a power that takes effect after the first attack, I'd say that the first attack would have the +2 modifier, but any attacks after the first wouldn't.

Even though it takes place after the first attack, you have to declare that you will be using the power prior to making the attack. Hence, if you use the power, no Back Alley Brawl, period.

This is a great question. Unlike a lot of special powers, Cap does not have to take an action to specifically activate Followthrough. Specifically, I'm not sure you DO have to declare Followthrough when you make a simple cc action against Cap's first target. I think Cap could get the BAB bonus on his first attack (assuming it was a straight-up no power cc action), but not on any Followthrough attacks.

First off, what does Cap's special power say?

"When an attack by Captain America KO's an opposing character, he may immediately make a close combat attack against another adjacent opposing character as a free action"

The word immediately is the key. It does not say 'after this attack is resolved'

Immediately means as an action within an action (like unstoppable's wall attack), before the action is completed. In other words, if you were pushing, you would finish your free attack then take the push

Because the power states immediately, it is part of the action.

So, no, BAB and this power are a no go

If you want the BAB bonus you do it without any powers (Passive or otherwise) or Team Abilities on the character.