Since atmospheric pressure is very large, so we just have to create vaccuum on one side of the transport to make it go to that side by a large force. And, the size of the vaccuum doesn't even matter. A few millimeters thick vaccuum would lose the contact of atmosphere from one side of the vehicle. I hope some vaccuum creating devices have been invented by now. Now, those devices have to do work on air to move it by a few millimeters and create vaccuum there. We'll derive that energy required by the device from the kinetic energy of the vehicle itself.
Suppose we create some initial vaccuum on top of the vehicle upto a few meters by spending some energy. The vechicle will move up and will require some kinetic energy. And, we'll give some of this kinetic energy to the vaccuum creating device to produce some more vaccuum. I hope machines have been invented to convert kinetic energy of the vehicle to heat to give to the vaccuum creating device. And once the vehicle has acquired some kinetic energy from the initially created vaccuum, the vaccuum creating device has to maintain a 1mm vaccuum for the rest of the journey, the energy for which it will acquire from the kinetic energy of the vehicle itself. And, work done to move air through some millimeters against atmospheric pressure should be less than the kinetic energy of the vehicle if the lower cross sectional area of the vehicle is large.
And once the vehicle has acquired a convenient height, we'll somewhat let the air fill in the space above it to the extent that the lower atmospheric pressure balances its weight. And then we'll create vaccuum towards one of its horizontal faces to move it horizontally.
What are the flaws in the idea?
I have used the word 'vaccuum' while writing all this. But we don't even need complete vaccuum. Atmospheric pressure is very large. So, even removing 50% of the air above should give a good pressure difference.