It's the button on the left bottom edge of the screen.
Tap on it and it becomes orange - shuffle is engaged.
Tap on it again and it shuffle is disengaged.
I have a playlist created with VLC on windows stored on a NAS shared folder. WHen I play the playlist in VLC for iOS, and have randomized turned on, it plays the first song sequentially. If I click next, it skips to the next album. Random is certainly turned on but I am fairly certain the only random thing it is doing is picking to play the start of a new sub folder from 1.
Does VLC for iOS randomization only work if all files are in one folder? I prefer to use sub folders for files I wish to play. The playlist I use contains relative links to the files.