Hi there. I suffered from chronic blushing for years. I know how bad it can be.
I didn't have any success with CBT or psychotherapy. I still have therapy, but it didn't do anything for the blushing.
For me, the best solution has been the MAOI antidepressant Nardil. Since starting it over a year ago, my blushing has totally gone away.
Other medications worth trying first are the beta-blocker propranolol and the benzodiazepine clonazepam. A combo of 40mg propranolol and 0.125mg clonazepam daily was a help for a while before I started Nardil.