That’s a really good question…one that I’m going to attempt to answer (but may fail to adequately address). While I have SEVERAL Alexa devices in my house (and even a handful that I carry around with me), I do not own a Kindle Fire, so my experience with that particular device will be entirely speculation.
Assuming that your Kindle Fire is associated with the same Amazon account that you developed and deployed the skill with, it SHOULD just work. But, I can see a few gotchas that might prevent it from working.
When you asked Alexa to open “Star Port Seventy Five”, she may have misheard what you said as something else that (at least to Alexa) sounded like “Star Sport & Sub”. After all, those two things are named such that they sound similar. Moreover, the Kindle Fire doesn’t quite have the same level of sophisticated array of microphones that a real device would have, so the likelihood of being misheard is greater.
One thing you might try doing is going into the Alexa Companion app or https://alexa.amazon.com and go to the “Skills” section. From there find the “Star Sport & Sub” skill and disable it. This will give you a slightly better chance of hitting the right skill the next time you try.
If you’re still struggling, you could try changing the skill’s invocation name to something completely different to see if you have better luck.
Of course, it might also be that the device isn’t associated with the same account that the skill was deployed with. So, as you asked, how can you know? The best way to find out, I’d think, is to sign into https://alexa.amazon.com or into the companion application on iOS or Android and go to the “Devices” section (on the website, I think it’s under “Settings” if I recall correctly). Be sure to sign into the Alexa website or companion app with the same credentials as you signed into developer.amazon.com when setting up the ASK CLI. If the Kindle Fire is listed, then it’s probably a matter of Alexa mishearing what you said. If the Kindle Fire isn’t listed, then that device must be associated with some other account.
One other thing: You say that the only Alexa device you own is the Kindle Fire, but you could have a few others you didn’t think about. If you have the Alexa companion app installed on your phone, it can also be used as an Alexa device. If you have an Apple Watch or iPhone, you can also install Voice in a Can and use it as an Alexa device. I’ve also tinkered a little with an app called Ally for iOS which turns your phone into an Alexa device. And then there’s the Developer Console, which gives you the chance to speak to Alexa (or type at her if you prefer) that serves as a device.