The flickering interferes with the polarity inversion done in the LCD to reduces image retention, with some models of panel being more sensitive than others.
I don’t know the exact timings for the N64 but I checked the optimized mode for it in the OSSC Pro. There the sample rate is set to 773.5 samples per line and 640×240 active pixels, so that could be a starting point for the OSSC Classic as well (the other parameters don’t carry over directly from the OSSC Pro to OSSC Classic.)
Given that the horizontal sync in 480i is 4.7 µs out of about 63.55 µs, the horizontal sync length should be set to around 57 or 58 and vertical sync left at 3. From there you can then adjust the horizontal and vertical backporches to align the picture.
For the PS1, from what I can find the sample rate should be 853.25 (rounded to either .20 or .30 I guess) with an active area of 640×240 and a horizontal sync of 63. The dot clock reportedly varies between hardware revisions though, so it might not be correct for your PS1.
Hope it helps. 🙂