sync mail folders between desktop and iphone
The problem you are having is because the folders are on your Mac rather than in one of your Google accounts.

If you want to be able to read the emails on your iPhone they will have to be on the Google IMAP server.

Can I suggest you get one of the two Google accounts to forward its email to the other account. Then you could put the folders in that account and they would be on the Google servers and accessible from anywhere you want.

You can even set it up so that you can choose which of the two accounts is sending any email you send, even from the one account.