I have the same kindle and also the same problem but it's interesting to note that the virgin staff don't really know what they are talking about as the Kindle HD 8 runs the OS 18.104.22.168 which is above their minimum spec. As they obviously didn't read your post properly when they quite clearly blow you off with the standard reply about earlier models which yours (and mine) clearly isn't. I do know that the app works on my home network after a fashion but doesn't work if you change networks which is why we use it because if we are at home we don't need it! I also run (or try to) the app on a new Samsung Tablet, Samsung Galaxy S8 and a Samsung Galaxy S7 all which run OS 7 or above and guess what the app don't work on any of them so in my opinion VM either don't care or don't have a clue what they are talking about.
Pardon my vent it's maddening when people change things for the so called better and can't be bothered to test or give proper support for the rubbish they bring out.
so in conclusion please try the link below see if it helps you any, it's more than you will get form virgin support it may work for you unfortunately it don't for me.
You're spot on with your thoughts on the response I received.
Thanks for the link on out of home streaming.
Initially I gave up trying to use my kindle to access virgin tv channels, but more recently, when the virgin apps changed (& kindle OS was the only platform not to be supported by virgin), I decided to install Google Play on my kindle. I followed the instructions at the following link, and now have access to all the Google Play apps, including the Virgin Go app:-
Initially, it was a little flaky but after a few days, it settled down & now is great. I can now access all the channels I normally subscribe to, including BT Sports, although Sky Sports is still proving a bit more challenging!