Yes, you can use Bikeflights to ship a battery-powered electric unicycle (e-unicycle). Because an e-unicycle contains a battery, it is subject to the same shipping standards that apply to shipping electric bikes (e-bikes) with Bikeflights.

When booking an e-unicycle shipment, select “Complete E-Bike With Battery Installed” from the “Contents” drop-down menu.

E-unicycles contain lithium ion batteries, which are potentially hazardous; if they are damaged, they can catch fire or explode. Therefore, you MUST follow additional e-bike-specific packing instructions before shipping your e-unicycle.

Because e-unicycles have lithium ion batteries, they can be shipped only via ground service within the contiguous US. They CANNOT be shipped to Alaska or Hawaii or via air service or internationally.
Shipping of mopeds, Vespas and motorcycles with Bikeflights is prohibited.

See related items:
Can I ship my e-scooter with Bikeflights?
Can I ship my Onewheel with Bikeflights?