If a single member limited liability company (“SMLLC”) elects to be disregarded for federal tax purposes, can its corporate parent claim the SMLLC’s job tax credits on future franchise, excise tax returns?

No.  Tax credits are specific to the entity that earned them.  If a SMLLC with a corporate parent has elected to be a regarded entity and earns job tax credits, the credits are being earned by the SMLLC that files a franchise, excise tax return.  If the SMLLC later elects to become a disregarded entity and be treated as a division of its parent, the parent is not entitled to claim job tax credits the SMLLC earned as a regarded entity.