The de Rham space of a scheme is essentially never a scheme or algebraic space (unless I guess you're Spec of an Artin ring, in which case you'll get a discrete set of points). In particular this applies to the flag variety. I'm not sure which perspective of NC AG you're taking, but certainly if you define the field as the study of Grothendieck categories, or pretriangulated dg categories, etc then D-modules are a very nice (nonproper) noncommutative space. (An interesting comment on this is found at the end of Kontsevich's letter here. Also from the point of view of "function theory" D-modules on a scheme are great, i.e. all functors are given by integral transforms, sheaves on a (fiber) product are tensor product of categories of sheaves, etc, see here.) But I don't think this says anything about the de Rham stack in a classical commutative sense..
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