What happens if a dog eats flour?

Nothing serious. The dog won't eat much of it (it's tasteless) and it is nutritionally sound.

If for some reason the dog did eat a lot of it, it's still not actually poisonous, but you should probably monitor the dog for the next few days. If he's acting (and pooping) normally, then he's probably fine. If he's acting like he's in pain or has difficulties, then take him to see a vet.