Example program:

{-# LANGUAGE TypeInType, KindSignatures, ExplicitForAll #-}
import Data.Kind
data X (a :: forall k. k -> * ) = X

errors with

polykind.hs:3:1: error:
    Expecting one more argument to ‘a’
    Expected kind ‘k0’, but ‘a’ has kind ‘forall k. k -> *’

Without TypeInType, the error is better, yet gives false hint:

polykind.hs:3:23: error:
    Illegal kind: forall k. k -> *
    Did you mean to enable TypeInType?

For the record 7.10.3 doesn't recognise polymorphic kinds at all (same program, without Data.Kind import):

polykind.hs:3:23: parse error on input ‘forall’

Which makes me think that polymorphic kinds are somehow supported, but maybe not.