Google search terms "ammunition site:aa.com" yielded:
http://www.aa.com/i18n/travelInforma...e/firearms.jsp
Transporting Firearms And Ammunition
Note: American Airlines does not accept firearms in checked baggage to/from the United Kingdom (except for military/government personnel with proper documentation).
The information shown below pertains to travel within the United States only (unless stated otherwise). For information on the transportation of firearms and ammunition to international destinations, please contact Reservations.
General Information
* Firearms and ammunition are accepted as checked baggage only.
* Firearms will only be accepted if unloaded and in a locked, hard-sided container only (for example - rifle case. TSA approved locks are now accepted).
* Ammunition must be packed in its original packaging. Loose ammunition or clips will not be accepted.
* Firearms may not be checked curbside.
* No one under 18 years of age may check a firearm.
* Pellet and BB guns are not considered firearms, and therefore, do not require any special handling or documentation.
Allowance
* Maximum per case is three rifles/shotguns or five pistols/revolvers, five lbs. ammunition, shooting mat, noise suppressors, and tools. There is no limit on the amount of cases allowed.
* Ammunition is limited to 11 lbs. per passenger.
* Charges may apply based on the number of checked bags in addition to oversize/overweight charges. Visit the Baggage Allowance page for more information.
The TSA
pages on firearms do not claim declaration is required for ammunition, only the firearms themselves.
You would probably be better off contacting American directly to see if they expect you to declare the items at check-in.