"Flew" is the most correct, "Flied" sounds really strange, and Flowed is the past participle of Flow e.g. The water flowed
"Flown" is a word I would use to describe something flying, e.g. "The plane has flown away", whilst "flew" is what I would use to say that I had taken part in the flying, e.g. "We flew to Mallorca at 5 PM".