Yeah, washing bedding and vacuuming is necessary. Especially get around the edges of the floorboards with the crevasse tool. The dog house too if you have one outside. There are also electric flea traps. As for the dog, I don't know of any home remedies.You might want to try the health food store and see if they have anything. Getting rid of the fleas is more important at this point, tho I understand why you want to avoid chemicals.
I had a problem with fleas when my dog's medicine stopped working (they became immune to the medicine) and we used Dawn Dish Soap to wash him. It killed them instantly, but it was only a temporary fix.