Kittens - well, cats in general - have very sensitive stomachs so the cause could be any of the following more common reason:
1. Adult/regular tinned cat food.
Kittens need to be fed a kitten food for at least the first 6mths. All the supermarkets do their own brand of this and it is worth giving the kitten the best start with "baby" food.
2. Milk.
Cats are lactose intolerant and so cows milk is a BIG no no no as it will give them the runs within hours of having milk.
If you want to feed your cat milk then either buy the Cat Milk that is found in the shops OR you can give them human Lactose Free milk .... this is pretty much the same composition as cat milk and this tip was given to me by all 3 of the vets I have had in various areas of the UK. Its brand name is LACTOLITE.
3. Finally, worms!
Make sure you get your kitten wormed as they will be more susseptible to all sorts of upsets if they aren't.
Hope this helps. xxxx