You should not flare with stopping MTX for one week.
MTX has a body life of 6 weeks, with it reducing in strength every week.
This means that if you miss taking it for a week, then you still have some MTX within your system, to keep on fighting for you.
Also, your specialist would not say it, if they thought it would be an issue.
Maybe the bigger issue, is taking your MTX and the vaccine at the same time.