No fly fishing experience out of Cancun, so hopefully someone else can come along and give you some better recommendations. I was in Cancun earlier this year before I got into fly fishing. Walked down to the rocks at the southern end of the hotel zone (21.036911N 86.777596W) with a spinning reel in the mornings and caught a bunch of small jacks while my wife slept in. Locals were hand-lining assorted snappers with 2-3" sardines for bait. Not a bad DIY option if you want to sneak a few hours of fishing time in.
We did an excursion down to Punta Allen for a panga ride / snorkel trip. It's a very long trip to make in a day from Cancun (~3hrs one way), but just seeing the Sian Kaan biosphere made it worth the trip. The flats and reef are amazing, and I hear the fishing is awesome. No first hand reports, but I'm planning on getting back there to fly fish in the future. Saw a fishing resort called pesca maya in the biosphere and they do day trips out of Cancun
http://www.pescamaya.com/en/daytrips.html.
If you found a way to get to Punta Allen yourself, I think you could rent a panga like the one below (our ride for the day) for a couple hundred dollars a day.