Probably the definitive study of bullet stability in flight is by Brian Litz in his book "Applied Ballistics for Long Range Shooting".
His analysis begins at about p. 159.
There was a post/discussion on stability on the old Forum, and I believe it was transferred to this new Forum.
You might try searching for "Stability"?
In a nutshell:
The RPMs of a bullet decays more slowly than velocity as the bullet travels forward in distance. A bullet's gyroscopic stability actually increases for a while as the bullet travels forward.
Dynamic instability increases as the bullet slows down and becomes transonic in speed. This occurs at about 1300 fps and for most modern centerfire cartridges, at about 1,000 yds distance.
Basically, stability is a product of both barrel twist and velocity.