Parrots who do not play on the ground or floor will not usually get fleas from a dog.
My suggestion is you buy something for fleas for your dog. Fleas are very nasty creatures and drink the blood of your pets. They will eventually make the dog sick and it will die.
There are a lot of flea medications on the market. There is Advantage, Frontline Plus. DO NOT USE ADVANTIX OR BIO SPOT AS MANY DOGS HAVE DIED FROM AN INGREDIENT USED IN BOTH OF THOSE.
Keep your birds up off the floor or ground, and they should be safe from fleas. Birds do get mites which are insects who also drink blood and are too small to see. Take your bird to Avian vet at least once a year to have it checked for infections and parasites.