When flow issues arise, flights that have not yet taken off get a specific release time (which can suffer further delays) - flights that are already in the air are already on their way. They may suffer vectoring, speed restriction, etc., but the landing slots are spoken for. Airlines are then told "you have X landing slots in time period Y" and it is up to the airline to decide what to do about it.

Simplistic terms, yes, but this is why LAX/SFO is more likely to be delayed than DEN/SFO, which is more likely to be delayed than ORD/SFO. The international heavies, as they are long on their way, get to land (unless it is so bad that diversions are in place).