All you answers can still be gotten from this your topic:
Best 2 Factor Authorization for Coinbase and GeminiBut where is the backup key that I need to write down if something happens to my phone?
I am not a Coinbase user, but the 16 character code should be along the QR code that was provided on Coinbase, that is the backup. You can also backup the QR code.
Could I install google authenticator on two devices at the same time?
Even you can install google authenticator on many device and all would work appropriately but installing it on two or more devices will not be appropriate and reduce your safety, for security and safety reasons, best to just have the authentication app on a single device which should not be the device you used for your Coinbase account.
Even if I could do that, I want a way to restore my coinbase for google authenticator.
hosseinimr93 has provided enough information needed about that, you can follow what he posted above.
How do I do this? I thought there was a long key you need to write down on paper as your backup? So if anything happens to your phone, you could just enter that long key to restore it... that isn't how it works with google authenticator?
I will advice you not to use Google authenticator because it is close source, but you can use the QR code export to backup as many as possible character codes which can be imported into another authentication app.
But if you need the 16 character code which can be used for recovery, you can import the google authenticator QR code on Aegis.
I will recommend you to use Aegis, it is open source and working perfectly.
The QR code is only recommended for exporting on another device which you can also be able to do it on Aegis. For backup, on Aegis, at the upper right corner -> click on the three dots -> settings -> scroll down and click on 'export'. The files can be exported to a particular file location of your choice on your device which you can backup offline and delete from the file location. It can be in .json which will be advisable to be encrypted. It can also be in .json or .txt in unencrypted format.
So far you just want to get the 16 character code, you can use the unencrypted, back it up offline and delete the text file on your device.
Or go to the exchange or wallet to change the authentication so it can generate new one for you that you can backup offline. You should be able to see the QR code and the 16 character code together.