Does the fire tv stick work with an iMac 2014 computer. I am using the mini display port with a HDMI adapter. I am getting no connection

the port of the imac is only an input for other target display port supporting MAC computers, for all other purposes it's an display output port

https://support.apple.com/guide/mac-help/use-an-imac-as-a-display-mh30822/mac

Why would you need one? You can stream pretty much anything you can access on a fire stick on the web.