A truly uniform distribution, no. (Well, your question is not completely well posed, but I will argue this for most ways of making it so.) There are $n!$ (kn)!$ factorial ways to shuffle a deck of $(kn)!$ kn$ cards. So you want each permutation to occur with probability $1/n!$. 1/(kn)!$. In particular, for every prime $p \leq kn$, you want $p$ to occur in the denominator of the probability that each permutation occurs. Let's look at your operations: Reordering $i$ decks can only introduce primes $\leq i$. Perfectly shuffling an $n$ card deck can only introduce primes $\leq n$. Cutting depends on what mathematical model you use for cutting; if all cut points are equally likely, you only get primes dividing $n(n-1)\ldots (n-i+1)$. I imagine other models of cutting will cause similar problems.
The more commonly studied question is how to get a probability distribution that is extremely close to random. There are lots of good results on this; see Trailing the Dovetail Shuffle to its Lair.
