I see... The KCFinder doesn't really have a good mobile design. The solution would be to update the design and add your own media queries to account for it. This is something I could help with in a premier support ticket.
You would probably want to hide the folder navigation by default and add a toggle button to display it when necessary. Then update the CSS for the image display to show on individual lines and drop the text from the buttons so they can fit more cleanly. It wouldn't be too difficult to pull off, but would probably take a good hour to work out.
Did this help? Tips are appreciated...
