You are not entitled to work or continue to work a second job while out in connection with a work injury or illness unless you receive written permission from the company. The company is not permitted to deny such a request unreasonably. Keep in mind that if you have a second job while working as a flight attendant, the wages from that job are included in calculating your average weekly wage and compensation benefits. Furthermore, all employers and their workers' compensation insurance companies are entitled to know about any wages you receive while disabled from a work injury.
For more information for injured American Airlines flight attendants, including company forms, contract provisions, and union guides, click here.