
Luke is an interesting mystic in that he's best when played to full hi-jinx and shenanigans. His stat line for both Mystic and Seeker is mediocre, so you're going to be most successful looking for ways to grab clues from the Dream-Gate that require little or no testing, and using his dippy do dah to avoid monsters and traps, or cause them to fizzle.
Some fun suggestions:
Gate Box + Vantage Point + Seeking Answers combo to pull two clues from a high shroud location with only auto-fail to stop you. With Seeking Answers (2) this can be done in one action. If you can boost the Camera while doing so, awesome! Play Enlightened on this Investigate to turn a card into a charge on anything but auto-fail.
Gate Box + Pathfinder to instantly teleport to any revealed location as a free action. You can set up some serious crazy with Shortcut, 2xPathfinder, and your Gate Box where you can Pathfinder into an unrevealed location, Shortcut into a second (use Shortcut second in case a monster spawns), then Gate Box shenanigans and use the second Pathfinder to pop out wherever with a full turn's worth of actions remaining and two additional revealed locations.
Alyssa Graham + Gate Box + Drawn to the Flame to pull two testless clues from a high shroud location when you find an encounter that can't spawn at your Dream-Gate. If you are the lead investigator, Alyssa can do a lot of work for the team by identifying location attachments, treacheries where X is based on shroud, and irritating no-VP monsters for you to negate. (Just remember to use the Gate Box during upkeep player window!).
Hemispheric Map + Gate Box + Read the Signs for an 11 skill test as long as four locations have been revealed (See Pathfinder/Shortcut above) - another two clues on basically anything but auto-fail. If you're rocking the Camera from earlier as well this could mean even -8 is no biggie.
Working a Hunch basically any time you're at the Dream-Gate and won't be using your once per turn ability on something else.
I have found that when I play Luke my partner is often annoyed that it's STILL MY TURN because I'm doing so many free trigger actions. That's typically the best sign of a successful shenanigan - your game group can't believe you still have actions left.