to start off I am by no means an expert on the fire tv stick, I would do as jitterjames recommends and double check your settings
, and I would add double check your network connection* (More bellow)
but this is what I can tell you from my experience with FTV (Fire TV) stick
VC
CAN connect to Kodi Running on a Fire stick just like every other version (Platform) of Kodi (using XJson.SetConnection action)
*how ever if the fire stick disconnects from the network for any reason then you have to navigate to the FTV stick home screen and wait for it to reconnect or go into network settings and select your network so it will connect. during this time VC
CAN NOT connect to kodi because kodi does not have a network connection, if you want to check your network connection from within Kodi, you can try and play a media file that is located on your network, if it plays then you have a network connection. if it does not play then you need to reconnect to your network
the FTV Stick can get slow when having VC do multiple things to Kodi, for example: starting an addon and then adjusting the volume in Kodi immediately after can cause some of the volume adjustments to get lost, so some commands may need to have a delay added (VC.Pause) to the steps, this is not due to VC or Network speed, this is due to the FTV stick's CPU power
while streaming bigger files with the FTV stick (2+ gigs) over the network you can see a delayed communication between VC and Kodi on the FTV stick (this doesn't happen every time but the FTV stick is the only place I have it happen on my network)
I hope this information will help with your trouble shooting