Background: I am trying to work out some Ext calculations for finite flat group schemes over a ring where p is nilpotent. I know how to do these calculations for finite group schemes over a finite field $k$ using the anti-equivalence with Dieudonne modules. I also know how to do this for finite flat group schemes over the ring of Witt vectors $W(k)$ by using the anti-equivalence with finite Honda systems.

Question: Is there a similar anti-equivalence that classifies finite flat group schemes over a ring where $p$ is nilpotent?

(Although this is probably no simpler, I would be satisfied with knowing the answer when $p^2 = 0$.)