fastest way to sample many random permutations of a numpy array
You can use rng.permuted instead of rng.permutation and combine it with np.tile so to repeat x multiple times and shuffle each replicates independently. Here is how:
perms = rng.permuted(np.tile(x, n).reshape(n,x.size), axis=1)
This is about 10 times faster on my machine than your initial code.