Welcome Jason.
It depends on where you store the videos and how large the videos are. Most likely an app like this would be very limited.
YouTube is hosted on servers to stream data. You can mimic YouTube by
- making a website hosted on a server that will store your videos
- link to the content videos using App Inventor and the VideoPlayer component possibly.
or
Using App Inventor you might be able to store videos on GoogleDrive then use your app to select which video and play it on your Android using the VideoPlayer component.
or
Link to a video on YouTube using [HOWTO] 📹 YouTube Video Player With App Inventor!
What have you tried?