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.
To supplement Amrita's answer, you do:
Open Android phone settings.
Go to Apps.
Find and select Chrome to open App info.
Click on Storage to view storage details.
Click on Manage Storage to manage the storage.
Click on Clear all data to wipe account details from the browser.
Relaunch Chrome, Accept & Continue.
Select desired account from the drop-down and click Yes, I'm in.