I think you'd end up with much higher quality if you used a dedicated film to digital converter (like these) or had it professionally transferred and then imported the clean digital image into PD. See these discusions for more info (or search the forum for 8mm film):

https://forum.cyberlink.com/forum/posts/list/83564.page
https://forum.cyberlink.com/forum/posts/list/38802.page

Here's a discussion using a set up like you've described but with a variable speed projector. Without that, I think you'll end up with many projector shutter artifacts showing up and making those recorded frames unusable.

There's also the issue of recording a projection from a screen, which would be of lower quality than what you'd get by scanning each film frame directly, although if there are lots of scratches or other imperfections on the film itself then you might actually prefer the softer screen recording.

I'm going to assume that the answer to
my question about whether PD 14 can remove flicker from a video is
“no,” as well as the answer to the question about whether there
is a guide to editing 8mm movie transfers as also being “no.”

I looked at the discussions you linked
in your response, and, with the post about 2K ProRes, I could learn
that stuff, but it's way over my head for now.

I agree with you that the best quality
would come from professional labs or a frame by frame machine.
However, I have 62 reels of film, so the cheapest lab I could find online
would cost me $570 (with a 25% discount), and frame by
frame equipment (in the link you sent) such as Eyesen, Kodak and
Wolverine costs up to $400. My approach costs me nothing additional. None
of the cheaper machines (<$168) from your link looked very good,
and they didn't give specific details on how a reel of film would be
transferred. I don't want to end up sitting there pressing a copy
button for each of what I estimate to be +178,550 frames on 62 rolls
of film.

The real question is whether my
relatives and I would get some $600 worth of enjoyment out of high
quality copies of these home movies, or, as I'm pretty sure they'd
say, “Are you loopy for spending that kind of money when your
camera produces stuff that's good enough?” Or, maybe I should ask
them and let them decide...

Thanks much for your advice and the
quick response. Stay safe.

Quote I'm going to assume that the answer to my question about whether PD 14 can remove flicker from a video is “no,”

You're right that that the cause of the flicker is from the projector's shutter, and when you capture with your "free" set up you'll have 100s or 1000s of frames from each roll of film that are at least partially blocked by the shutter. I'm not aware of any way for any version of PD to automatically remove them.

You could remove each one manually on the timeline, but then you'll be skipping frames left and right and I think the only thing all that work would get you would be to trade most of the flickering for sections that skip ahead too quickly.

You'd also have to spend a significant amount of time for every single roll of film you captured, and even if you work for free - at some point I think your time is worth a couple hundred dollars on a project this size.

Making that investment would get all the frames transferred cleanly (and automatically) and then you could spend your time editing and producing the video the way you want it to look.

This is all just my opinion and there are other forum members who have vastly more experience transferring flim than I do, but there's always a price to pay for projects like this and I think there's a clear justification to spend some money on the right equipment. Maybe even ask the relatives to help you out by donating to the cause so you can focus on the main task

Removing flicker is a task best left to Avisynth or Vaporsynth code. Powerdirector doesn't get anywhere near that stuff and it's a pity.
The best for this is maybe Hybrid free software, but it's got a learning curve. VirtualDub is also a good choice.
The other issue is MOV, a compressed file type, and every time you mess with it and render it's another round of lossy compression.
You may want to convert your files to lossless HuffYUV or MagicYUV or even Lagareth before attempting restoration, and keep outputting lossless results until you get it looking how you think it should look, and THEN bring that lossless repaired file into PD for final edits and delivery. HP Envy Phoenix/4thGen i7-4770(4@3.4GHz~turbo>3.9)
Nvidia GTX 960(4GB)/16GB DDR3/
Canon Vixia HV30/HF-M40/HF-M41/HF-G20/Olympus E-PL5.
Tape capture using 6 VCR, TBC-1000, Elite BVP4+, Sony D8 camcorder with TBC.
https://www.facebook.com/BarryAFTT

Just starting to transfer the 8mm this week and I found a way to eliminate the flicker...
Playing at 18fps, use a camera capable of a shutter speed of 1/55. For me, this was only my galaxy note 9 running ProcamX (lite is free, but limits recs to 5min). I project onto white card stock (I tried about 10 devices and screen materials first),and zoom record with the phone.
Sometimes wb tungsten setting works best, and often tapping iso settings up and down during the projection works best.
My only post production is framing zooming and cutting. Good luck! I'll update if I ever get around to youtubing this info.