I just got a new kitten, 7 weeks old. He has been in the house for about 2-3 days and has gone pee multiple times and pooped once. He is litter trained, but he has been chewing on litter. I am unsure if he has been swallowing this litter and how often he chews on it. I cannot see a vet until next month. When should I be worried about this litter blocking his system? Is this a common or does this easily occur with a few grains?
It's not unusual for kittens to chew on litter - especially if teething (as Mick referred to in his comment). Try providing him with easy access to something else to chew on (you can get chewy kitten "treats" designed for just this) and in the meantime I'd change the litter to a non-clumping variety immediately - even if he is not trying to "eat" the litter there remains a risk that he will swallow some and clumping litter can be quite harmful if swallowed.
My parents dogs (which are litter trained) did that, too. So we changed the kind of the litter. We found a brand they did not eat, so everything is fine know.
Eating litter is something you should worry about, especially when it is clumping litter, because it can block his system. This depends on how much he is eating. So you should observe him until you found a brand you are sure he is not eating, and stop him whenever you see him chewing on the litter. A small amount should not be harmful, so don't panic, but watch him carefully.
Does he eat and drink enough? Is he active? Has he alternatives to chew on and enough to eat? If you see any changes in his behavior, e.g. he is calmer and stops eating and drinking, than you have to go immediately to the vet. But if he is acting fine, you should not worry too much.