Magnetic field of earth is ~50µT, a superconducting loop with diameter 1m (circumference ~3,14m) with 100kA will feel a force of ~15N, with 1cm² it has a volume of 0,314 liters, in aluminium thats about 0,85kg or 8,5N, in copper thats about 3kg or 30N. So with a material density of 5kg/dm³ or less it could be possible to fly. Changing the current in the superconducting coil to control lift and propulsion could be tricky though.