Your link takes me to a place where you can look up AMA chartered CLUBS....NOT flying fields as the OP's question read.
Clubs have flying fields (0 to many relationship). Flying fields are typically in the general vicinity of the club. After the searching for a club (http://www.modelaircraft.org/clubsearch.aspx) click on the club and then click on the "Flying Site Details" link, if available, to see the flying site "registered" with the AMA for that club. The process simple and easy.
Not ALL AMA chartered clubs have fields......
I didn't say they did.
But thanks for attacking my point. You do it well!
Not attacking, educating.
Thanks for playing,
No problem at all.
Astro