Will a Royal Poinciana tree survive in Jacksonville Beach, FL?

Answer 1

I would say no.

http://www.floridata.com/ref/d/delo_reg.cfm
Hardiness: USDA Zones 10 - 12. Royal poinciana should not be exposed to temperatures below about 45ºF (7.2ºC).

http://www.usna.usda.gov/Hardzone/hzm-se1.html
Duval County has always been classified in Zone 9.

Answer 2

It's a beautiful tree; I think it would be worth a try (particularly if you are close to the coast) if your cold winters only occasionally get below 45F