Aircraft companies experimented with similar ideas in the '50s and '60s. The end result was the modern hovercraft. They found that the setup was much more efficient with a simple rubber skirt to hold the air under pressure, and took far less power to maintain a hover. What happens is that unless you trap the air and force it to remain beneath the craft, it mostly "squirts out" in every direction shortly after it leaves the duct.

One of the first hurdles I see is getting an adequate thrust to weight ratio. It won't be so bad if you run it with an external power supply and umbilical cord, but if you want it self-contained, the batteries might make the craft too heavy to fly.

Another potential hurdle is maintaining balance. The three lift motors won't automatically produce the exact same thrust, and environmental conditions (e.g. uneven surfaces) will throw the craft off balance, so you won't always need the exact same thrust. You'll either need a more sophisticated radio, like a heli radio with CCPM mixing, or you'll need to design a gyro-driven system that automatically stabilizes the platform so you can control forward motion and steering with a simple pistol-grip transmitter.

Before you go spending money on fancy carbon fiber EDF units and hot brushless motors, you might want to build a prototype using inexpensive brushed can motors driving large props through gear reduction, with an external battery and "umbilical" for power. That way you can develop your control system and get a general idea of what the project requires without spending a bundle.