There's not significant enough evidence to prove covid19 vaccines cause a flare. Ancedotally a few think they might have. However, correlation doesn't necessarily prove causation. It could be coincidental, as we tend to associate any last change for the reason for a flare. When flares are months in the making, not due to something recent.
I am also not aware of any kind of published research yet on the matter, only sporadic announcements about
evidence that it doesn't seem likely to flare after the vaccine if you have UC. So it's equally anecdotal. The only one I know of is the one about
RA and it found out that some people experienced flares after taking the vaccine.
As for "correlation doesn't necessarily prove causation", it goes the other way around too.
Lastly flares are not always months in the making. Exposure can cause a flare for example.
I would take the vaccine again and again as it means my chances of developing severe covid are lower though.