OP, I totally get your question.
I know that the term has been around for many years as pointed out previously.
However, only RECENTLY I am seeing the term "flagship" included in the pricing options on AA.com.

Since the term was NEVER used in the pricing page (that I know of), I was also wondering if there is anything special about those fares with the "Flagship" term next to them.
See below for LAX-LHR pricing (only the non-stop AA operated flights show it).



I think it is kind of confusing because further below, the LAX-DFW-LHR option is shown like this:


Flagship is not mentioned anywhere. I know that the LAX-DFW is just a regular domestic first class, but the DFW-LHR is on a 77W and should be "Flagship" as well (note that the same is true for flights via JFK, ORD)
Even after clicking on details the term "Flagship" is not mentioned anywhere.
So this would make me think that if I go via Dallas (or other hub), I won't get the flagship product at all on the DFW-LHR flight.
But If you search for DFW-LHR only, then AA50 will show up as "Flagship".

It is confusing indeed as it is now.