How do I copy a personal DVD-R to a flash drive on MacBook Pro?

That depends on how the DVD-R was created.

If it has created as a playable movie disc, you will need to to use a converter app such as Handbrake to rip the video out of the DVD and copy it onto the USB drive.

https://handbrake.fr/

If the movie was just copied as a single video file onto the DVD-R you can simply drag it form there onto the USB drive Finder.

What do you see when you access the DVD-R in Finder exactly?

Do you see a "VIDEO_TS" folder?

Or do you see something else?

You can, but it won't just play from the USB drive if you do that.

You will need at an app to rip it. The Video_TS indicates the DVD-R was created as a video disc to play in DVD players.

You will need a 3rd party app lie Handbrake as I mentioned above to get the contents and convert it into a regular video file.