Nearly every big U.S. airline plans to apply for Cuba flights (http://www.usatoday.com/story/travel/flights/todayinthesky/2016/02/16/nearly-every-big-us-airline-plans-apply-cuba-flights/80468328/)
Miami and FLL are sure to benefit, will Jax?
It's hard to imagine an airline using one of the coveted slots for a Jax connection, but sure it would definitely be great if that could happen.
Someone from JetBlue was on NPR Morning Edition today discussing their bid for slots. I'm sure they'd fly out of FLL too.
Besides, Jacksonville already has flights to Cuba. You can catch the Patriot Express GTMO rotator out of NAS JAX (Cecil for now I guess).