Is there any way to switch Chrome profiles while using the Chrome mobile phone app?
There is no way to change Chrome profiles on Android/iOS as per Google Chrome Help here.
But, you can use apps like Parallel Space to have multiple chrome profiles.
There is supposed to be:
If you open Chrome on Android, Menu, Settings, and select your account.
But this just takes you on an endless loop.
I wish changing your user on the phone settings would also change all your apps to log in as that user.