I was wondering the same thing. I tried to link
BlueIris to my Alexa account using the steps detailed
here, but it really looks like all you can do is set Blue Iris options (change profiles, turn cameras on and off, etc.), not actually view streaming video from the cameras on your Alexa Show or other Alexa device with a screen.
That made me sad for a while, but then I realized that all of my cameras are just streaming RTSP video to Blue Iris, so why can't I capture that stream directly on the Alexa (basically bypassing Blue Iris)? Turns out this is totally possible, and I have it working now for all my POE IP cameras! The down-side is that since Blue Iris is my DVR, and I'm not actually connecting to Blue Iris to view video from the cameras, I'm limited to looking at LIVE video ONLY (i.e. you can't view recordings from the past) on your Alexa. But I don't really want to do that anyway. I just want to see who's at the front door "right now" or what my dogs are doing in the back yard (normally digging up my begonias).
I registered an account with
https://monoclecam.com/, and entered my cameras IP addresses and connection URL's there, then added the MonocleCam skill to Alexa. Instantly Alexa detected all my cameras, and I can ask it to "Show me the Front Door" or "Show me the Garage" to have the current live stream over RTSP show up on my Alexa screen.
Since I don't allow inbound connections to my IP cameras through my firewall, even though my camera information is registered on the Monocle site, no one could use it to view my streams from outside of my home network. All that the camera registration on the Monocle site does is provide the 192.168.x.x IP address and connection string to my Alexa (which is inside my firewall, and can connect to the camera streams just fine).
Oh, and if you have trouble figuring out what the cameras RTSP connection port and URL is, you can get it directly from your Blue Iris software. Just open the Admin UI for Blue Iris, select the camera you want info on, and click the Camera Properties button. From there go to the Video tab and click the Configure button. The IP address, port numbers and video path URL are all on that screen.
Good Luck!