If I may suggest: try the Google keyboard and/or chrome browser. Both are available in the play store for free and @Alenya Al'Roran says it works for her.
To clarify, I open the gif in a new tab/browser window and copy the link to that tab (the gif source url). Then I paste that url into the image link button pop-up window that appears when I click on the button just to the right of the smiley face above the reply box.
Maybe that method could...
My mobile keyboard has a gif button that I use. I just click the link and paste it in.
Maybe I'm doing it the hard way that's been explained and the simpler solution is the query at hand?