You can find subtasks of a parent using off the shelf JQL. I haven't seen anything else for the other way round.
Have a look at the JQL Tricks Plugin, a commercial one. it certainly has a method you can use.
I am afraid there is nothing in onDemand using which you can get this. Parent is however a field on the issue and hence you can use remote APIs (or CLI) to get this. You don't need JQL for it. Did you try that?
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