First, a private file does not involve checkout/checkin, so if you are talking about actual private files, you won"t have any co/ci operation to worry about.
This is different when you want to make local modification (ie modifications you don't intent to checkin ever) to tracked elements. Then you need to checkout, or to eclipse files (dynamic views) or to hijack them (snapshot view).
Second, as long as use the same dynamic view in a Jenkins job, the private files should be preserved (in the dynamic view vws storage) accross build, as long as you don't activate any "cleanup before build" option.
But if it is still not maintained, then you need to explore if it is possible to generate those private files in another shared dedicated filesystem, which would then be outside of any ClearCase view.