I have searched the entire yard and house for anything he could have eaten however, I have found nothing out of te ordinary. Is it possible for dogs to have the "flu"?

Yes,
Try giving him wet dog food, or dry food with an egg cracked over it. My 5 year old pekanise has really bad allergies and when his nose gets to stuffy he won't eat.. weird I know but dogs are a lot like us.

As the owner of an almost ten year old german shepherd I can tell you they a funny eaters.And sometimes they just are not hungry. I always feed him at the same general time and the same amount daily ( he gets a mix of two brands of dry food) if he eats it all great if not I leave the bowl down if he wants more he will eat if not I add more to equal his daily amount and set his bowl down again. Not drinking is a problem though I would let the vet check him out. I always figure better safe .
German shepherds are known to have delicate digestive systems so adding food to get them to eat is genarally not a good idea .I think the best advice about your dogs needs come for a good relationship with your vet.
My dog ate the same food for over eight years until it was recalled. Finding a new brand that worked for him was a nightmare that lasted sevearl months. But working with my vet and a combo of holistic and a store brand he is in good health for almost a year now.
Lets us know how he is doing.