Yes, termites fly.
I think the bugs you found by the dog food may be a grain beetle. They are very small and brown. I think they can just form in grain foods - even people grain foods like cereal. That is, if they are what I'm thinking of. The reason I say they can form in grain foods is because (this is going to gross everyone out) that all grain foods, if I remember correctly, do have tiny insects that you can't see in them.
