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Select the Vortex force and animate its position such that it moves in the XY plane inside the Simulator.

Here are the exact key-frames in case you'd like your setup to be identical to this tutorial. Also, set the tangents for the animation curves to Linear inside the Curve Editor. The default interpolation is Ease-In / Ease-Out which would cause to vortex to accelerate and decelerate unnaturally.

Frame 0:

X: -78
Y: 35
Z: -70

Frame 70:

X: 2
Y: -73
Z: -70

Frame 130:

X: 40
Y: 10
Z: -70

Frame 200:

X: -88
Y: -156
Z: -70

Add a Noise modifier to the shelled Poly Plane.

Set the Scale to 134, and the X/Y/Z Strength to 456 / 127 / 77.

Enable Fractal and leave the Roughness to 0 and the Iterations to 6.

Make sure to Enable the Animate Noise option.

You may also open the Graph Editors → Track View - Curve Editor and set the tangents for the Phase parameter to Linear.

Select the Phoenix Source and set the Emit Mode to Volume Inject. The Volume Inject mode emits fluid into the container with pressure such that expansion occurs immediately after emission. This will further randomize the fire right at the source.

Set the Noise to 0.5. The Noise parameter acts as a random multiplier for the Inject Power.

Now that we've got Fuel, Temperature and Smoke injected into the simulation and carried by the Vortex force, the fiery tornado is finally starting to take shape.

One major issue to address is that the smoke can be clearly seen travelling straight up. This is caused by the Gravity setting in the Dynamics tab. With Fire/Smoke Simulations, cold smoke (Temperature lower than 300 Kelvin) falls down and hot smoke rises up. This is causing the funnel of the tornado to break-up in an unnatural way. There are 2 ways to go about fixing this:

1. You can try increasing the Axial Drop / Orbital Speed / Radial Pull parameters on the Vortex Force to counteract gravity. This would likely be the 'physically correct' way to go about doing this - the vortex should be strong enough to have full influence over the trajectory. However, this could also turn into a time-consuming endeavor.
2. You can simply disable Gravity.

We go with the second approach.

Uncheck the tickbox to the left of Gravity to disable it.

Set Time Scale to 0.9 to marginally slow down the simulation. This will give it a more epic appearance.

Smoke Dissipation should also be increased a bit. Set it to 0.1.

The dissipation of the smoke allows for interesting details to form while the smoke channel is carried through the cells of the simulator by the velocities present in the simulation.

Set the Conservation Mode to Buffered.

The Buffered conservation mode is ideal for fire simulations because it tends to give the most detail. It appears as if it 'chops up' the fluid as it is transferred through the cells.

Disable Uniform Density and Set the Quality to 80.

Uniform Density controls whether the mass of the fluid is considered during the calculation. The mass is calculated as the inverse of the temperature - hot fluid is lighter and cold fluid is heavier. Since we disabled Gravity anyway, this won't do us any good. Disabling should save some time during the simulation.

The Conservation Quality controls how accurately the fluid is transferred through the cells of the Simulator. When this value is low, some of the fluid is lost along the way due to the nature of how grid-based simulations work.

Select the Vortex Force and increase the Axial Drop, Orbital Speed and Radial Pull parameters. How strong you make those is entirely up to your artistic judgement.

In this example, we set them to the following values:

Axial Drop: 48
Orbital Speed: 48
Radial Pull: 12

Lastly, open the Output rollout of the Simulator and enable the export of Velocity.

The Velocity channel is required when rendering with Motion Blur so V-Ray knows in what direction to 'stretch' the fluid.

Create a Helpers → Phoenix FD → PHXTurbulence.

Set the Strength to 250 and the Size to 914.

Reduce the Fractal Depth to 0.

The Turbulence is used to break-up the fire even further. Please check the comparison images below.

To create the bullet-time effect, open the Dynamics tab of the Phoenix Simulator and animate the Time Scale parameter as follows:

Frame 1: 0.9
Frame 48: 0.9
Frame 92: 0.1
Frame 117: 0.1
Frame 150: 0.9

The Time Scale is a global multiplier for the dynamics of the Simulator. Reducing it will uniformly scale down all sources of velocity in the simulation.

Consider settings the tangents to Linear in the Curve Editor - the default ease-in / ease-out may look unnatural.