Family Sharing and Roku

I am not clear as to what your issue is here. Are you trying to get a free trial, or are you trying to sign into Apple TV on a Roku device (I don't know what you mean when you say "Roku" since I only know a Roku device as an item of hardware)?

If your issue is signing into the shared AppleTV service, carefully read: All the ways to watch Apple TV+ - Apple Support

If you're trying to sign into a trial, check these links for tips:

"Get 3 months of Apple TV+ for free." - Click on the link and read it, including the FAQ at the end. Check your eligibility. --> https://offers.appletvapp.apple/

"Only one offer per Apple ID and only one offer per family if you're part of a Family Sharing group, regardless of the number of devices you or your family purchases. "

'If you can't redeem your promotional trial of Apple TV+' click here --> If you can't redeem your promotion for an Apple subscription - Apple Support:

See if this page helps:

https://support.roku.com/article/360036652634

and the links on this page Get the Apple TV app or Apple TV+ app on your smart TV, streaming device, or game console - Apple Support

If you still have questions or problems:

Contact Apple. Click here --> Choose your country or region - Official Apple Support Select your country, then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.

or:

Contact Apple for support and service --> "See a list of Apple phone numbers around the world."

Click here --> Contact Apple for support and service - Apple Support