Anyone know why dark matter wouldn't be rotating along with the rest of the galaxy?
No one knows if dark matter exists and what it's made of, so you can make as many assumptions as you want to help your fancy research as long as it doesn't contradict other observations.
Dark matter is matter. It gravitates. It obeys conservation of angular momentum. Unless the dark matter clump happened to form in a spherically symmetric contraction, it will be rotating, almost certainly coupled to the rotation of the galaxy.
The entire reason that spiral galaxies exist is that baryonic matter interacts electromagnetically and can dissipate kinetic energy via heat (photons). That causes matter to eventually flatten into a disc rotating more-or-less uniformly.
In this sense a DM halo is similar to elliptical galaxies which certainly have net angular momentum, but their stars have essentially random orbital planes.
Does this take into account frame-dragging induced rotation?