To watch live TV you'll need to install the TVPlayer app:
https://tvplayer.com/
You can use it for free to get all of the channels shown here [except as below] but you'll see ads from TVPlayer:
http://tvplayer.com/channels
[Note that licensing rights problems mean that you WON'T get channels operated by UKTV when using the app on an Amazon Fire TV Stick. So you'll lose Dave, Yesterday, Really, Home and Drama, together with their 'plus 1' channels, where appropriate].
However you can pay 99p per month to get the service without seeing ads from TVPlus.
. . . or you can pay £5.99 per month to receive an extra 24 subscription-only channels, such as Eurosport 1 & 2, Discovery, National Geographic, comedy Central, etc (The offer appears to give you 29 additional channels but, once again, you'll lose the UKTV channels because you're using an Amazon Fire TV Stick. So, for example, you won't get Gold or W).