Does the referee have to accept my flag decision?

No. Under Law 6 the referee controls the assistant referees or touch judges, may tell them what their duties are and may overrule their decisions. The referee may alter a decision after you have raised the flag to signal touch or touch-in-goal, or after you have signalled foul play. It is also for the referee, not you, to decide whether the ball was thrown in from the correct place.

If a touch judge is unsatisfactory the referee may ask for a replacement, and if the referee believes a touch judge is guilty of misconduct, the referee has the power to send the touch judge off and make a report to the match organiser.