Hey Julian,
this is fine, then you can supply your 220 V VFD directly from a NEMA 14 or NEMA 6 socket. What you need to know for the connection of the VFD and the spindle as the next step is described here in this post:
Also you should
- Properly ground your machine and the VFD control cabinet
- Recommendations for NOT soldering spindle cable connector
- Manufacturing a spindle cable
Here you can see some additional parts you could also use to reduce electromagnetic interference and to make the three-phase current that the VFD delivers less noisy and less harmful (approaching the ideal of nice sine waves). The most important is the matching EMI filter, usually its part number is mentioned in the VFD manual.