On mobile, click on the green menu icon in the upper left corner. Then scroll down to "User Image Upload Manager". The interface isn't ideal for mobile, but should work. Hopefully, you don't have any issues scrolling down with the upper left menu bar. I've seen that before and don't yet have a solution.
Once you upload images with the tool, you can click on the XIMG tag that will let you easily select the image and will insert the code for the image wherever your cursor is placed.
Here's an example... I'm doing it from my iPhone:
View media item 29017
I just uploaded it in another browser tab, and then went to select it. I even had started this post before switching tabs, taking the screen capture on my iPhone, and uploading.