A few things about how we are using TouchID in the app.
TouchID is something that needs to be set up in your phone/iPad Settings or as part of the initial iPhone/iPad setup process on capable phones (5S and later). Once set up on your device, you will then need to sign in to Frame.io to activate TouchID for the app. After the initial sign-in, TouchID should be enabled by default.
Check that TouchID is enabled in the app's internal settings (go to the Profile tab, tap the Settings button in the upper right, and make sure the TouchID switch is on).
After signing in (either using TouchID or email/password), the app will be unlocked for the remainder of the session (i.e., you will not need to use TouchID to get in until your device ends the current session of the app and starts a new one).
If none of these apply (you have signed in and the next time you open the app, you are brought to the sign-in screen with no TouchID pop-up), try double-tapping the Home button (opens iPhone/iPad app switcher mode), swipe up on Frame.io to end the current session, and try reopening the app.