For this, you could use our pressure transfer system. 

This has an attachment that connects to the lid of the Conical Fermenter by a tri-clamp and allows co2 to be used to put pressure in the headspace. You can then either use the dip tube that comes with this kit, or the dual valve to move the beer from the fermenter through the silicone hosing provided.

To move it to your keg without air exposure, you would need to pressurise the keg to a higher pressure than the fermenter and attach a corny disconnect to the other end of the silicone tubing that your beer will be flowing through. When that’s hooked up to the beer outpost of your keg, you then use the PRV on the keg to balance the pressures.

When the pressure is greater in the fermenter than that of the keg, the beer will start to flow, and fill the keg from the bottom.