Problem:
I am building a directory website with UNCODE and Toolset. Registered users can update their profiles or submitted projects with Toolsets frontend (CRED) forms.

However, the "upload media buttons" on these forms do not work with UNCODE. Is switched to the Twenty Twelve theme and it worked without problems.
Solution:
I made a lot of tests, cleaned my site further more, cleaned the database, re-installed the theme etc. Then I compared my installation to yours in detail.

As I checked every setting of the UNCODE theme one by one I found out that a single setting to "Disable MediaElement Player" in the "Performance"-Tab of the "Theme Options" caused the script conflict (see https://powerful-theremin.sandbox.otgs.work/wp-admin/admin.php?page=uncode-options and the attached screenshot).

When this setting is "ON", even in your sandbox installation, the upload media button isn't working any more.