Balk after pitch
 

Astros vs Rangers on 6-10. Texas closer clearly balks (he tried to quick pitch and never came set) with a runner on third but it is missed and the pitch happens. After the pitch the manager comes out and argues for a balk. The umpires get together and call a "retroactive" balk, for lack of a better term.

Is calling a balk after the fact (pitch) allowed? What is the procedure for handling such a call? How would you have handled it?

Yes, it's allowed -- and it's handled just as you described (umpires get together, review what happened, decide the ruling)

Are umpires slow to call that, like applying advantage in soccer? I saw a quick pitch in a FED game that wasn't called, but the batter got a single and an RBI from that pitch.

They shouldn't be slow to call it, but in the case you present, even if it was called it would be ignored in a non-FED game.

In this case the manager came out to ask if the pitcher declared he was pitching from the windup or the stretch. Crew got together to ask if F1 declared he was in the windup. He did not so they called the balk.

I think I have seen MLB crews ignore the MLBUM instruction to call time and announce the windup to both dugouts and the crew which did not happen but if this crew was lax in following that instruction it would make sense that they would get together. What does not make sense is on the pitch in question the windup could not be declared. Kela had already started pitching from the set to that same batter after the runners advanced to 3B and 2B. You can't change with the same batter unless the runner config changes and you announce at that point.