Umm... from Jackie Chan himself, out of his own mouth on the outtakes/interview part of one of his movies. He said that all of his moves come from watching bruce lee or other martial artists in film. The only reference I could find to him getting any type of martial arts training is the wikipedia page on him. The source is from a biography from
Star Pulse:
Enrolled in the Chinese Opera Research Institute at the age of seven, he spent the next decade in rigorous training for a career with the Peking Opera, excelling in martial arts and acrobatics.
If I recall the interview correctly, he said that he found he was very good at acrobatics and action sequences and trained to do that type of acting. Note that this is not martial arts training but more of an "action oriented acting training".