My drain in the basement backed up now I got millions of tiny black bugs in the carpet if I walk through they are all over my ankles and my dog is infested what do I do?

Doesn't sound like drain knats on your dog, sounds like fleas.

None of the small insects that feed on sewage also infest mammals. They may ride on your dog, but they'll fly or fall off at the least provocation. You may have two problems that just happened to show up at the same time.