To upload your GIFs on Instagram you will need to convert it to a video and then email it to yourself (so that you can get it on your phone and post on Instagram).
Giphy makes this process incredibly simple so we highly recommend you use this solution while we develop our own sharing technology.
1. Go to http://giphy.com/upload
2. Upload your GIF
3. Follow these steps to share your GIF on Instagram via Giphy