Is he still FLA property?
No, he's a UFA but he's played in the NHL before, so he has to follow the regular UFA rules. Usually player contracts have to include the current season, with 3 exceptions that are allowed to sign earlier:
A) Contract extension
B) Unsigned Draft Pick
C) Draft-Related UFA
Shipachyov falls under (C) because he's never played in the NHL before, so he can sign a contract now that starts next season. Dadonov who was signed to an NHL contract in 2009 by Florida and played in the AHL/NHL until 2011-12 does not fit into any of the exceptions.
It's the same reason Kovalchuk can't sign until July 1st--he doesn't fit into an exception either. Likewise Radulov had to wait until July 1st to sign with Montreal last summer.
The League Year runs July 1st through June 30th.
edit: Here's the relevant CBA section for those interested:
CBA 50.8(d) Prohibited SPC Terms and Practices. No Club or Player may enter into an SPC that does not cover at least the then current League Year. The foregoing does not apply to an SPC entered into pursuant to Section 50.5(f) above, or to Unsigned Draft Choices or Draft Related Unrestricted Free Agents, who shall be permitted to sign an SPC during the period from March 1 through June 1 immediately preceding the League Year in which such SPC is to take effect.
Section 50.5(f) covers Contract Extensions. The language defining Draft-Related UFA's can be found in CBA 8.4 and 10.1(d).