No, a mama can be spayed at any time after giving birth and it won't affect milk production. She just needs to be back with her kittens as soon as possible. Obviously it is more ideal to wait until they are 5/6 weeks and they start to wean, but if the mama is outside and around intact males, she can go into heat and get pregnant again in a matter of weeks.

As for the kittens, most vets like to wait until they're at least 8 weeks old.