This is not correct (if you are implementing Fisher-Yates algorithm), you should pick a second index j in the range i <= j < length list .

I was actually implementing the Knuth shuffle (see here) and it's really hard not to copy the code straight so this was the best I could do.

If you know shuffling algorithms which are faster or easier to implement in FP, please let me know. The current one is not very efficient: nth and rotatef both have O(n).
The knuth shuffle seems to be designed for arrays instead of lists.
Bogo sort is, on the other hand, not exactly made to be very efficient.

The Knuth shuffle is another name for Fisher-Yates. You have to either loop for i from 0 to length list - 2 and pick j from i to length list - 1 (incl) OR loop for i from length list - 1 to 0 and pick j from 0 to i (incl). Right now you're doing a mix of both.

And yeah, it's not very efficient. In my Haskell implementation I transformed the list into a map, made the n swaps, and back into a list. Going through an array would possibly be better, I'm not sure.

Lists are horrible data structures in many cases, but they are simple, it's fine for learning.

I think I got the shuffle method down, (I even found a nice shortcut for in- and decrementing by one) and I'm not going to bother using arrays. Lists are clear and easy to use and this is bogo sort after all.

This should be <= I think