the playing part in the app could be handled with a webview or a dedicated player (eg, exoplayer). obviously, the users need authorization (no problem).
the tricky part is how you deliver these videos: stream or download. either way involves bandwidth (money). having a list of videos available for download is the easiest on the server side, but not particularly pleasant for the user (although, once downloaded, they can be viewed as often as desired.) the size of the
videos could be an issue, depending on how big they are and how many a user is allowed/able to store on the device.
streaming videos is the most convenient for the user, but can be quite a production on the server side. if you expect your client base to be in the millions, you need to pay somebody to help you with the many choices available. that part has absolutely nothing to do with b4x or your app. it's a matter of scale and how much money you have to invest. almost any major streaming service can stream videos in one form or another that are easily handled by an app. and in many cases, the user could simply use her desktop browser as well. i watch live and canned videos every day on my device. from the point of view of the device, it doesn't care how much it's costing somebody else to stream those videos (that's why there are so many advertisements). that's your biggest concern.
youtube might be an option. not quite as impressive as having your own app, but a lot of people use the service. i don't know if google wants you running a business with it, but you could collect your membership fees as a separate transaction and then authorize people to view your "channel" on youtube. i'm sure you can find fitness channels on youtube to see what that looks like. there seems to be a channel for everything else, and people are making money.