Materials that last
Carcasses in marine-grade polymer, stainless steel or masonry. Not standard cabinetry, and not standard MDF-cored anything. Surfaces in sealed stone, porcelain or concrete. Stainless hardware throughout, because ordinary fixings will bleed rust down a stone front within a year.
Build it wet
Assume every part of it will get rained on and design the drainage accordingly. Cabinet bases that drain rather than pool, doors that shed water away from the carcass, and no detail that relies on a roof always keeping the rain off, because in a Florida afternoon it will not.
The services an outdoor kitchen needs
A GFCI-protected circuit to the Florida Building Code, a gas run if there is a built-in grill, and water and drainage if there is a sink. All permitted and inspected. A grill enclosed in combustible framing without the clearances the manufacturer specifies is a genuine hazard and one we see.
Where it goes
Under the lanai roof it lasts longer and is usable in rain. Out in the open it needs more from the materials. Either works; the choice changes the specification.