Jet on Sky Missions:
First you must complete the Free Mission at Shinjuku, after you comple Chapter Thirteen. Once the Free Mission is completed, a Jet will be unlocked that can be used during Sky Missions.
When you want to select the jet scroll all the way down on the Dragon Select menu (past the Chaos Dragon) and you'll find a option. Select it, and in the mission you'll be flying the Jet.