first thing you need to do after catching all the kits is baby proof that cage with hardware cloth from a place like home depot and remove all shelves from the cage, and then go out and buy a second cage for your male chinchilla. the mom and dad need separated asap, because you don't want to continue breeding chinchillas that don't have a pedigree/ have unknown health issues in their lineage.
mark your calendar 111 days from now, because if dad was in with mom before, during, and after delivery of the babies then there is a very high chance that the mom has been bred back already (female chins go into heat right before/during/after delivery). a chinchilla's gestation period is approximately 111 days long.
with four kits i would get yourself ready for hand feedings, just in case, as momma may not have enough working nipples or enough milk for them all. there are many breeders here on the forum that can help you with what supplies you will need and how to go about it. one other essential item to buy is a digital kitchen scale that weighs in grams, so that you can track and monitor the babies weight to ensure they are gaining.
most of the reading i've done on weaning age says 8 weeks as long as the kit is in good weight, healthy, and doing well. male kits need to be separated from the female kits and momma at this age, to prevent them from breeding with either.
other members here will have much more detailed advice, and hopefully will chime in soon.