How to Avail 3 month Apple TV free trial with the purchase of my Roku TV?

Also note on the Roku page of the offer that FoxFifth provided the link for:

Valid only for new subscribers to Apple TV+ in your region

So if you have used a free trial anytime before for the Apple TV+ service, you will not be eligible.

Apple Trials are only available for new subscribers so if you had previously subscribed, you won't be able to claim the offer. I would recommend contacting your Roku support if you haven't used Apple TV before, and are having problems.

See the following from https://www.roku.com/deals/appletv

How do I sign up for this offer?

Be sure to opt-in to Roku emails to receive you redemption code.