Not all AAdvantage credit cards offer free baggage. Example: I have a AA Citibank MileUp card, not free baggage.
"American Airlines-affiliated credit cards that typically provide a free first checked bag on domestic American Airlines flights include the Citi® / AAdvantage® Platinum Select® World Elite Mastercard®, the Citi® / AAdvantage® Executive World Elite Mastercard®, the AAdvantage® Aviator® Red World Elite Mastercard®, and the Citi® / AAdvantage® Business™ World Elite Mastercard®. The specific benefits, such as the number of companions receiving the free bag, can vary between cards, so checking the details for each card is essential.