I was surprised to see that DirecTV Stream still supports the Stick model 3500, as some developers have dropped support, but checking their Website, they still support that device. https://www.directv.com/support/stream/article/KM1200941/
It should be there. My guess is that DirecTV Stream made an error in the last update to their device, and didn't include the 3500 as a supported device (an error, it seems).
You see, app developers can pick and choose what devices they support. If they leave a device out of the listing in the update, the device won't see the app as an option to add, and it won't get added if it's tied to the account in another way (Website Channel Store, another Roku on the same account, etc.).
Just in case, do a reboot of the Stick. But if that doesn't work, it could be that you'd need to reach out to DirecTV Stream to ensure there's not an error in the app that's keeping it from showing for the model 3500.
Roku Community Streaming Expert
Note: I am not a Roku employee.
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