Yes. I've seen reports of mutation rates that are 1/2 to 1/3 that of the flu, but also commentary that direct comparisons might not be as relevant, since influenza has multiple "segments" that SARS-CoV-2 doesn't and these segments allow more "shuffling" and more impactful mutations.
One thing is absolutely true: the greater the transmission rate, the greater the mutation rate, so getting transmission rates down (via vaccination, preferably and not contracting the disease) is critical to slowing viral mutations, which should make it less likely that new variants evolve which can "escape" the vaccines.
The other positive factor in play for humanity is that our bodies have memory B cells which remember antigens like viruses, but that these also evolve, producing antibodies in the future that wouldn't be produced today, meaning it's possible that future variants might still be defeated by the evolving immune response triggered by the original vaccine (Derek Lowe did a nice write-up on this that I linked a few weeks ago).
https://www.the-scientist.com/news-opinion/a-guide-to-emerging-sars-cov-2-variants-68387