Sorry not on xbox although I haven't tried it on there but once you recorded a clip either on a pc or laptop goto xboxdvr type in gamertag and you can view pics/videos of your own. there should be an option to convert to gif in imgur. I've noticed lately that it can take a while to upload clips on xbone live
EDIT:
I should point out that a 2nd hand kinect camera should be pretty cheap now and it records the last 30 seconds of a gameplay almost effortlessly. I just shout out "XBOX RECORD THAT" and that's it.
To add on to this you can also Double tap the Guide button and press X instead of using a kinect/mic.
Also in All Settings>Preferences>GameDVR&Streaming you can set your xbox to recored the last 15sec/30sec/1min/3min/5 minutes of gameplay.