If it is thick and chunky like coffee grounds it could be earmites which will need medication from a vet. They have to go to the vet at 8 weeks to start their vaccine series so you could just ask the vet to take a look and clean them at that time right?
In the meantime, a drop or two of mineral oil on a cotton ball will clean off the surface dirt, but your kitten does need to see a vet for those vaccinations and a check for mites.