I have a 2017 Wahoo Kickr which doesn't allow for a Sram xdr driver...but I now have all Sram Red AXS eTap 12 speed. Since the Kickr will accommodate a Shimano spline, can I put on a 12 speed Shimano cassette and run a 12 speed Shimano chain and still use my Sram shifters and front chainrings?
TLDR: officially no.
Chain compatibility becomes a bit messy from 12 speed.
SRAM has two kinds of 12 speed chains: "standard" and "flattop" (used on the Red AXS), that are officially not cross-compatible (rollers are larger with flattop). The standard one is the most direct evolution of the "11-speed chain", and most brands such as KMC are following that spec.
Shimano on the other hand has changed the tooth profile on the 12-speed systems (road and MTB, called Hyperglide+) to allow downshifting under tension. The exact specs are not known, but it looks like the inside width is narrower and the profile of the plates is different.
The solution you propose (non-flattop chain on a flattop chainring) is the least "mechanically incompatible" solution. But even if it works, shifting performance and wear on the chainring are likely to be impacted.
Also another point: SRAM are sizing their chainrings considering a 10T small sprocket, not 11T, so the ratios with a Shimano cassette on a SRAM chainring will be closer to gravel ones than road ones.
I'd search for alternative solutions instead.
UPDATE: SRAM has released 12-speed 11-44 (CS-PG-1231-D1), that uses the standard Shimano HG Spline and are compatible with flattop chains. It won't work for a 2x setup, but for a 1x gravel setup, that works.
Another possible solution would be to get a Hyperglide-compatible cassette and a 12s chain with standard roller size. It is more expense. The AXS jockey wheels are not quite shaped for the smaller rollers of a standard chain, but the jockey wheels are under very little load.
Consistent with what Renaud said, Josh Poertner said here that he had tried a DA chain on an AXS system, and shifting was not optimal, and he implies that his wear rate was higher.
A more extreme solution might be possible if someone can identify which original equipment manufacturer supplied the 2017 Kickr's freehub body. For example, many OEM hubs that are unlabeled or branded to a company that doesn't make their own hubs are made by Joytech, Novatec, or a few other mainly Taiwanese companies. You would then have to find some way to acquire an XDR hub body compatible with the Kickr. Those companies may or may not be set up to sell direct to consumers - that is, they typically deal with wheel manufacturers, although sometimes you can buy their hubs from wheelbuilders. In fact, it does seem like Wahoo could have provided the manufacturer information to consumers to let them update their freehubs.