Members can submit an unlimited number of videos. As of today, there is no way to limit members to one video but you can submit a request to let us know you want this!
There a few ways you can limit member videos:
Freeze Topics for View-Only
Flipgrid does provide the ability for leads to freeze Topics and make it view-only.
Moderate to Hide Videos
Additionally, Group leads can choose to approve all member activity. This will hide any new video Responses from the Group or Topic until the Group lead chooses to make it active.
It's also a great teaching moment to let your members know if they don't follow instructions, they will lose participation points!