TLDR : Help: can Sighthound work with MAnything? Or another app that only streams when there's movement?
Initially I tried setting the Fire up
without referring to the directions above - disastrous. I think there's a bug in Sighthound Video whenever "Other IP Camera" is selected. The screen shot below shows nonsense:
https://192.168.1.128:8080/192.168.1.128:8080
in the line
below the field for the Stream path. The form requires that I fill out both fields - IP address and Stream path, but if I do, that nonsense string appears.

After I followed the instructions - rather than specifying Other IP Camera, but otherwise using the same info, Sighthound Video was able to connect to the Fire, but only sporadically. I think my Wi-Fi network can't handle the video.
Testing UPDATE:: As I hoped, the Fire seems to be running IP Webcam and Manything fine despite Amazon's suspect claims of incompatibility.
I don't think Sighthound can work with MAnything, and I am hoping to have access to Sighthound's advanced video review and analysis features, so I'll only use anything if I can't get Sighthound Video and a webcam app working together.
With the Sighthound + IP Webcam app setup, the Fire is trying to stream video continuously, 24/7. I can't get it to stream video only when there's motion. It seems the Wi-Fi can't handle this. The connection rarely works - is not even close to stable. The video has to go over Wi-Fi from the Fire to the router AND from the router to my computer. It seems it can't handle two video streams on top of what it already has on it. Worse, IP Webcam streams video all the time. Just one camera ONLY streaming once to the Internet via Wi-Fi when there was movement was something the Wi-Fi was able to handle reasonably well when I was testing MAnything.
If I get Sighthound on a computer connected to a hard line (that is, via an Ethernet cable connection to the Internet) I can halve the amount of Wi-Fi bandwidth used and maybe Plan A will work well (IP Webcam and Sighthound Video)
As noted before, initially, the Fire refused to let me install any webcam software. This is because Amazon wants you to use it normally, so you end up buying lots of stuff from Amazon, especially media to view with the Fire. (See screen shot below - the red X shows that the Fire, which I've named "Nun's Fire" is supposedly not compatible with the webcam software.)

Anyway, hope this is helpful to others on this path, and hoping for answers/help: Can Sighthound be made work with MAnything? Or another app that only streams when there's movement?
I'll post pictures once I have a working system and/or catch a crook.