The effect only works if the slices line up exactly. A pixel of overlap and the join doubles up. A pixel of gap and a line appears. Cutting by eye in a design tool is where most attempts fall apart, because the cuts drift and nobody notices until the post is live.
So the cuts here are computed rather than eyeballed. Interior cut positions land on whole pixels, adjoining slices share an edge, and the last slice takes any remainder so nothing is dropped or duplicated. Rejoin the exported slides and you get the original back with no seam.
The second thing that breaks a seamless carousel is Instagram's own cropping. Every slide has to share one aspect ratio, and slides that do not match the first one get cropped to fit. That crop is uneven across slides, which is exactly what pulls a continuous picture out of alignment. Padding each slice onto an identical 1080 × 1350 px canvas removes the reason for the crop: a 1500 × 1000 slice becomes a 1500 × 1875 px slide, and so does every other slice.
A note on how it will actually look. Instagram shows a gap between slides as you swipe, so the picture reads as continuous rather than truly unbroken. Design for that: keep faces and important detail away from the joins, and let the background carry across them instead.
Up to 20 slides. Everything runs in your browser and nothing is uploaded.