No, I have never heard of such. I am not much for competition. I think it would be hard to find expert judges. Also the USA is so spread out, it would be hard on many to finance travel.
There has been an Annual Flamenco Expo Competition at Concurso Nacional de Flamenco (Festival Flamenco Internacional de Alburquerque) which has been held for many years at the University of New Mexico in Alburquerque. Unfortunately, Festival Flamenco Internacional de Alburquerque was suspended this year due to financial concerns related to the current economy. See: