How can I get cooking oil out of my bird's feathers?

I have a atiel bird. He has his wings clipped; got spooked when husband moved in bedroom and flew towards kitchen area to a pot that I was getting ready to pour used cooking oil (from couple of days before so not hot) from into milk jug, he was submerged from lil area of tummy, feet, all way down to tip of tail. Took him to shower and tried to get off what excess that I could get off, & used bird bath spray, that didn't seem to help. Have "Dawn" but wasn't sure about using that so needed something to adhere to oil....I used all purpose flour, that seems to have helped and feathers are not matting to him as if from being wet. What should I do next? was flour a good idea, or have I done something totally wrong here....he is a rescue bird & a good friend to have due to severe anxiety attacks; has helped a lot. Any suggestions would be GREATLY appreciated.