Scale it up big over 1000px like Kiana said and I don't even think it matters exactly how much. You do the same for animations in Photoshop, but instead of exporting them as GIF, you render to video (at the huge 1000px+ size). Personally I haven't had problems with this approach.
One extra thing to know with all this is: when a person browses posts on Instagram, they take a 1 sec look, flick to the next image, 1 sec look, flick … If something catches their attention you might get 3 or 5 seconds of their time. While you might care about perfectly sharp pixels, I guarantee you, nobody else does, including pixel art aficionados (I'm extrapolating a bit here, but you get the point). It used to be different in the early days of phones, but now with high density displays, it really isn't a big deal. The problem is only when beginners post native or barely upscaled sprites and they get upscaled by the platforms into a blurry mess.