What this means is, you can’t use another account to login into that Flipboard app on your device. For instance, if you have two Flipboard accounts in which you use email to log in, the first one you use on the app will be the one that can only be used. Another email account won’t work, this implies that you won’t be able to use your second Flipboard account on that device.
I had the problem when I first installed the app on my phone. I log in with one of my accounts and I thought I could log out and then log in with another account. But no way, it was not possible. I contacted the Flipboard team but the feedback didn’t help to resolve the problem.
After much efforts, I found a solution and it worked.
How to disable the Google Smart Lock on Flipboard
Login to passwords.google.com and turn off Smart Lock for Passwords
You can also delete the email account saved to the Flipboard app. With this, you can now log in with another Flipboard account on that app in your android phone.
I hope this works!