From the Citi site on my AAdvantage card:
Call 1-855-569-7399 within 30 days of the trip delay.
Download a claim form
Return your completed claim form and all requested documents within 90 days of the trip delay. You’ll be notified of the decision on your claim once it’s been processed.
Full coverage guide is
here.
Prestige page doesn't have a ton of information available, just says to call.