I have seen how-to-fill-aa-com, but I have pretty much same on Win, so I decided to post this here.
On the main American Airlines page aa.com login consists of three fields. 1P does not fill the middle - Last name . Then it takes me to the second attempt page https://aa.com/login/loginSubmit.do . There it already has the frequent flyer filled, and fills the last name and password correctly, and successfully autosubmits.
Win 7 SP1. FF 38.0.1