I attempted to sign into Dropbox via my iPhone and was unable to do so. First, let me describe my situation.
Now, when I attempted to make my initial sync with Dropbox, the Dropbox sign in webpage was displayed within the 1Password app, as I'd expect but I didn't remember my password or have it copied to the clipboard so I had to exit that screen, copy my password and return to the Dropbox sign in screen. Once I entered my information in the web view, I was prompted to enter my security code so I exited the app, opened Authy, and copied my access token. However, when I returned to the 1Password app, the sign in view was closed and by the time I could access the sign in page again, my token had expired.
To solve the problem, I downloaded the Dropbox app, signed in, and attempted to sync again. This time I could authenticate via the Dropbox app and didn't experience any issues.
To solve this issue in the long term, users need to be able to exit the 1Password app during authentication with Dropbox to copy their two factor author access tokens. Also, it would be nice to have the ability to automagically fill in the Dropbox account password when setting up Dropbox sync.