This doesn’t look like a ‘traditional’ distressed texture to me so much as some lossy gif compression artifacts. Probably the original animation just had some fake film grain added and that is playing havoc with the compression
if you do want animated distressed texture you could just paint and scan some rough black+white ink/watercolour washes and loop a few different ones (enough to not be tooo obvious that it’s a repeated loop) + overlay it on your whole animation with some transfer mode or other. Or download something similar from some free textures site. Probably you’d want to animate it on twos
Old cel animation doesn’t really have that kind of texture tho so it depends how realistic you are aiming for. At most and old film could be faded and damaged and you might get some dirt + scratches, if you want that look there’s plenty of good film dirt + grain overlays out there to download.