How to hide Dynamic Island while using apps on iPhone?

You cannot as your Face ID sensors and Camera are built into the Dynamic Island. The Dynamic Island should not be interfering with the app user interface, and if there are elements of the UI that are being blocked by the Dynamic Island, then the app needs to be updated. Developers do have control over the contents you see in the Dynamic Island, so they can use that space for additional info and they may allow you to change the contents you see.

You can't, but you might be able to temporarily hide it with some apps by swing left or right on the Dynamic Island.