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Florida Statute 320 deals with motor vehicles licenses. Section 320.01(1)(a) defines "motor vehicle" to not include traction engines, road rollers, vehicles that run only on a track, bicycles or mopeds. From what I know of razor bikes, they are most closely akin to mopeds, except that they have an electrical engine instead of gas.
Based upon the statutory definition, since the razor bike is not a "motor vehicle" it does not require a license. However, it might be advisable to call the Florida Highway Patrol Motor Vehicles Division at 904-225-9117 to see if the state's interpretation of the statute is different from the plain language of the statute (trust me, it happens).
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