Right, so you need to plug it into that, not the TV, since the TV can't send USB data to the Fire Cube that is running the app.
It looks like the Cube doesn't have any regular usb ports, so you'll need to use an OTG adapter like this one to connect the controller to the cube.
EDIT: Looking again it looks like the Cube has separate power and Micro USB ports, so you could use a hub like this to get yourself a couple extra ports
I have a Galaxy S5, so your phone should be a little smaller than mine. The first headset I bought was this. It was cheaper at the time. I found my phone had a little trouble fitting unless I removed its case. The case made it too thick.
Not long after that I ended up ripping the cardboard, so then I bought this. My only complaint about the second set is that there is not a magnet/washer for the apps which rely on it. That said, being able to adjust the interpupillary distance is very nice. If you have a USB controller you want to use with apps, I'd also recommend adding an OTG cable to your order.
Make sure the model you purchase has a head strap. It can ruin the immersion if you have to constantly hold the darn thing up. Hope that helps!
I use a cable exactly like that one and am having (mostly) zero issues so I don't think it's the cable itself. I am a firm believer that even via OTG any given flash stick or (micro) SD card is still hit or miss. I have four different microSD cards and several different adapters & I said "(mostly)" because my 4, 16, and 128 GB cards all work with every adapter.... but my 200GB card does not work with ANY of the adapters, at all. It just boots to stock despite the fact there's nothing wrong with that specific card.
All in all, I'd chalk the slowdown to either 1.) not enough power from whatever power source you are using, 2). a bad/corrupted/incompatible microSD card, 3.) a bad microSD reader/adapter, 4.) corrupt game files, or 5.) any combination of 1-4. I very much doubt it's the cable, but as I said... I think regardless of OTG the entire thing is STILL very finicky and picky. OTG does not equate guaranteed compatibility & I think too many people are under the assumption that it does - then are surprised when their stick or card doesn't work.
Here is the setup I have:
OTG Cable: https://www.amazon.com/gp/product/B00CXAC1ZW/
USB Hub: https://www.amazon.com/gp/product/B071JTSMVQ/
microSD Card: https://www.amazon.com/gp/product/B06XWZWYVP/
microSD Card Reader: https://www.amazon.com/gp/product/B07G5JV2B5/
I just tore the OTG Y cable apart, it doesn't work because there is no ground wire running to the micro USB male plug, this cable is meant only to externally power the attached devices, not the host device, or in our case, the nexus 7.
http://www.amazon.com/gp/product/B00CXAC1ZW/ref=oh_aui_detailpage_o02_s00?ie=UTF8&psc=1
I can confirm this one works for me: https://www.amazon.com/gp/product/B00CXAC1ZW/
But I think I'll order the 'Rii' cable that others have linked to 'cuz I like the layout of it MUCH more.
Hmm, that's a very interesting device. Note that I'm not an Android phone user, and I have no first-hand knowledge of the OTG protocol, but I see no reason why that device wouldn't work. It does a lot more than just interface USB to your phone, but at that low price point, there's no harm in getting it to see how it works.
If it were me, I would only buy an adapter that can be powered externally. When using a USB mic with a phone, you don't want to worry about how long your battery will last while driving both devices. You'd want to research this adapter to see if it can be powered, either via USB or other dedicated power supply.
Here's a simpler example of something that work: https://www.amazon.com/Micro-Cable-Samsung-Player-OTHERS/dp/B00CXAC1ZW
Be sure to search YouTube for videos about connecting USB mics to Android phones, also. There are many to look at. Best to you.