Hi all,
Right now, the plumbing work has been performed in the JuMP ecosystem to let you access the IIS/conflict-refiner functionality of your solver. More precisely, there is a low-level interface in MathOptInterface to ask the solver to compute a conflict and to retrieve whether a variable bound/constraint is part of the conflict. However, this feature is very low-level.
What is your workflow for dealing with infeasible models? What functionalities would you like JuMP to offer?
My workflow is to ask for a conflict, then export it in LP form, and analyse it manually. Do you do the same or do you have other workflows? The goal is to have an API that fits most (if not all) the needs in this area 
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(Just to be clear: the question is about a comfortable way to use JuMP when debugging infeasibilities. For now, providing an IIS solver that is completely independent from the solver is out of the question: the current implementation is relying on existing functionalities of the solver for that part, doing more would require much more work…)