Thank you all for your input and trying to help me out, I really appreciate it!
So, I've been doing a little more playing around with my setup. I noticed that on my second TV that has a 4th generation (non 4K) Apple TV attached some of the content that was previously flickering on my main setup with the 4K Apple TV was still flickering, but not nearly as bad. That led me to play around more with main TV/4K Apple TV setup.
I have a LG OLED TV and I discovered if I remove all motion enhancements that make motion smoother, the flickering goes away. Unfortunately, I'm then stuck with more choppy motion. My best guess at this point is that other people using Channels having slightly different setups with their TV, etc that make the flickering less noticeable or eliminate it all together.
I'm also guessing that WMC on my standalone computer is using a much superior deinterlacing algorithm due the hardware capabilities of my computer so even though I have all the motion enhancements enabled on my TV, the deinterlacing is superb and there is no flickering whatsoever. @tmm1, from what you said, it sounds like the 4K Apple TV just can't support a better deinterlacing algorithm?
Because I want to keep the motion enhancement features enabled on my TV, I guess I'll either have to deal with the flickering/flashing on 1080i sources or switch back to WMC. @tmm1, is there any option of having access to a beta version or something that will allow me to use a better deinterlacing algorithm? If that was available, I'd be interested in trying it to see if my 4K Apple TV holds up ok. It sounds like there are options within Channels to use software or hardware decoding on the Shield, is there anything like that for the Channels on the Apple TV that I just can't seem to find? I have a couple more days on my free trial so I'll play around with stuff a bit more and see what I can find out before I have to make my decision to stick with Channels or to try something else.