640x360 is good! Any size you can multiply evenly to get 1920x1080 should work great. Some other fitting sizes are 480x270 and 384x216. Real Flipnote Studio images are 320x240px, so that last one will be the closest!
As for the exports... hmm. I think you're right that it's a limitation in Krita. Many programs have trouble displaying pixel art textures on a large image previewed at a smaller size (ImageMagick has some examples).
Hope that helps!