Most DC drives do not have capacitors to generate reactive current, they draw current from the AC lines only. When the motor is moving slowly with high torque, the drive has to produce full current even though little work is being done. This current has to come directly from the line side. So, even though there is no power factor on the DC side (just high current and low voltage), a demand for reactive power is created on the line side.
Power factor definitely still applies to the load side of AC drives. The DC bus capacitors supply the reactive component of the current, so power factor is the same even though it's mostly mitigated on the line side. i.e. This means that the apparent output current of the drive can actually be higher than its input current.
Flux current is just another term for reactive current, magnetizing current, VARs, etc. I think you need to distinguish between accelerating from low speed using a contactor with a 60 Hz supply, (where you are in-rushing the motor) and accelerating using a VFD, which gradually increases the frequency to the motor so that the in-rush never occurs. E.g. if you're at 50% speed you probably have >300% current without a VFD, but with a VFD you have 100% current (for rated torque) and ~50% voltage. The difference is that the VFD runs at 50% frequency (30 Hz) for 50% speed, so the motor's torque-speed curve itself is shifted because steady state rated slip will now occur at about 30 Hz instead of at 60 Hz.
It's true that the flux current is mostly just circulating between the VFD capacitors and the motor field windings, but I think you're still missing that even the actual flux current at the motor is much less than if you were driving the motor at full frequency and half speed (not something you want to do on a regular basis, your motor will melt).