You will earn AA miles if the flight is booked as a codeshare (AA flight number), and in this case you would need to supply your AAdvantage number. You can book these flights directly from AA.

You will not earn AA miles if the flight is booked with a TN flight number, so whether you supply your AAdvantage number is irrelevant in this case (unless you have connecting segments on AA, etc.) and may even be harmful in that it could prevent you from claiming with another airline. For a simple round-trip, these flights generally won't be on AA-issued tickets.

Note that codeshares are often more expensive, so it is worth checking both options.