Yes, amazon.com/mytv activation works on all Roku models including Roku Express, Roku Streaming Stick, Roku Ultra, and smart TVs with Roku OS built in (like TCL Roku TVs).
It depends on whether the TV's Prime Video app is still updated. Generally, Samsung TVs from 2016+, LG TVs from 2014+, and Sony Android TVs from 2015+ are supported. For older TVs, connecting a Fire Stick or Roku is the best option.
If your device has the Amazon Prime Video app available, it will almost certainly work with amazon.com/mytv. The activation process is the same on every device. Check your device's app store for "Amazon Prime Video."