According to the AMA's website:
Mission: To promote the art and science of medicine and the betterment of public health.
Vision: To be an essential part of the professional life of every physician.
The American Medical Association helps doctors help patients by uniting physicians nationwide to work on the most important professional and public health issues.
AMA policy on issues in medicine and public health is decided through its democratic policy-making process, in the AMA House of Delegates.
The AMA's activities with for-profit entities are directed by AMA guidelines for corporate relationships, and its Internet products follow AMA guidelines for health and information Web sites. For information and inquires about advertising on the AMA’s Web site, please send an e-mail to webads@ama-assn.org.
The AMA seems to be more of a lobbyist group for medical professionals, not for credentials. Personally, I don't think that it would make a difference if your doctor were a member of the AMA or not.
I would, however, be more concerned if my doctor was board-certified in his or her specialty. You can check on that at www.abms.org.
I would also check if my doctor is a member of any professional organizations dealing with his or her specialty. Those organizations typically require their members to be board certified.
Also, don't depend on your insurance carrier's provider listing for accurate information. I have seen doctors lie about being board-certified and other things, and when I brought it up to my insurance carrier's customer service, they never acted upon it.
Another thing: if your doctor's office changes their doctors that frequently, they are either not paying or treating their physicians very well. Translation: newbies and not exactly the best or brightest either to get involved in a practice like that. Find a more competent doctor.