They way I look at Instagram is a place to show my work to a portion of the population who are and aren’t professionals. Among those are people who are not going to go to my Flickr Youtube or Vimeo pages. Wanting to show bits of my video work to those people. I looked into ways of uploading High Quality video to Instagram. After a bit of experimenting I found creating a Source video in FCPX at 640 x 640 and compressing it with MpegStream Clip (Which is free and awesome). Creating a H.264 MP4 version works the best for me. My phone is android and has a Micro SD card slot so its as easy as Copying the compressed video to the SD card and sharing to Instagram from the Android gallery.
Here are the two I’ve created so far With a possible third one on the way.