How can flicker from a slide projector be removed from existing video footage?
I didn't view the entire video, but from what I saw it looks like a series of static slides. You could grab a still frame from each slide and create a (say) five second repeat of that frame, and use it to cover the section in the video where that slide appears. Every editing package I'm aware of can do this.

Better yet, get the original slide stack and scan them, then do the same as above. You can correct for parallax etc and have more readable content.