You might have to stick with the browser version. 
Like, I mean, searching for gifs with your browser.
Then going to the actual page and scroll to see the link button (bottom left in screenshot) and tapping that.
Then pasting the URL.
(Caveat: There’s a relatively new gif format that’s basically a video, called gifv. I’m not sure if those and mp4s are supported, so this won’t always work.)
But this method is so frustrating! 
I need to stop using my phone now and switch to a mouse and keyboard before I toss my phone across the room. 
Edit: I’ve switched and I’m still frustrated at my phone.