Hey David!
I did a little research to find a solution for your case. Unfortunately, it seems there is not a component on Mendix to achieve that by default.
As you can see here, it is a similar question https://forum.mendix.com/link/space/mobile/questions/124097.
There you can find the explanation of why there aren't any video recording solution (or at least I didn't find any on the marketplace) and it is not recommended to store video on the Mendix file system (probably due to the size of the files).
However, it seems that you can create a custom component or javascript action to do the video recording.
Here you have the link to know how to build javascript actions:https://docs.mendix.com/howto/extensibility/build-javascript-actions/
Here you have an example with live video recording for chatting, so you can see it's doable on mendix: https://marketplace.mendix.com/link/component/113742
Please follow the guide to use Camera in Mendix Native app. Link shared below:
https://docs.mendix.com/appstore/widgets/camera