In search of a good home for your Fearless Flatfoot? Then give some consideration to everyone's favourite Heroic Hobo, "Ashcan" Pete.
The key element that makes this pairing good is Duke's combined Move and Investigate ability. When Pete uses his best friend to sniff out some info, he triggers the action at his current location, provokes attacks of opportunity at that location, then moves, and investigates his new location without provoking opportunity attacks. This is a fairly decent method of triggering Alice's ability safely in multiplayer; There are definitely going to be times when you and your team mates are split up, one of them has drawn a monster and there are clues at their location (the cluever was in the middle of investigating, the fighter was exploring, etc.), and they want you to come help them out. Alice and Duke's teamwork lets you do that: the move action you'd have had to spend getting there anyway becomes a combined move and investigate with a free testless damage if the investigation lands. As an extra bonus, if the enemy is engaged with your friend then you can deal this 1 point of damage without any risk to them, since it's both testless and not triggered by fighting. If all that's needed is 1 damage (perhaps to help your fighter reach a higher total when he takes his own turn, or to finish a battle that he started) then considerations like whether or not to spend an action engaging the enemy first are left entirely to the wayside; not bad.
However, there's a lot more to this match-up than just the Duke trigger that enables it!
First off, Alice gives a static +1 Book, and Pete jams on static intellect boosts, since they work with Duke's nose. If you were considering Dr Milan Christopher for this reason, then Alice Luxley could be a fun alternative.
Second off, Pete has a minor niche as "that guy who can soak damage that tries to go to specific non-investigator cards first", and while Alice can only take 1damage and 1 horror safely and that's nothing to write home about for a four-cost asset, it still plays into that niche. Want to keep your Plucky around for longer, or keep that Helpless Passenger alive? Alice aids in that goal.
Thirdly, since Alice exhausts to use her ability, Pete has the option to use his own power to ready her for a second bite at the cherry. Adding "investigate; deal 1 damage to an enemy at your location" to the options that Duke already gives him for value from his card discard ability is solid and broadens an already broad toolkit. Pete can certainly provide the tech to pull off multiple successful investigates in a turn, such as part of a Will to Survive turn.
Fourthly, if you need to make Alice's damage more reliable, red cards have got you covered. You can help yourself succeed with the likes of Lucky!, or discover clues even if you fail your check with the likes of Look What I Found!
Fifth, Pete's status as a Dunwhich investigator means that he can not only take 2x Alice, but any other three level 0 cards he might want, some or all of which can be strong tech for Alice from any sources Pete prefers. Scene of the Crime is probably the stand-out option here; Alice normally is of use to Pete as an offensive option, but Scene of the Crime is perfect for letting him use her on the defence. Since Pete can typically only fight with Duke at most twice in a turn anyway, giving up his first action to pull two clues and deal a testless damage is unlikely to bother him/ be unattractive compared to getting a third fight action in, and it reinforces his strengths as a hybrid.
Sixth, the unusual match up of cop and homeless man provides added benefits to some potential red jank that could be a lot of fun to play. If you can secure yourself a means of over-succeeding an evasion test then Belly of the Beast becomes a power move with Alice on the field - evade an enemy, discover a clue, and deal 1 damage to the enemy you just evaded! Hybrid perfection. Or, again assuming you can pull of an evade (perhaps you took that Plucky after all?) then you can Bait and Switch an enemy on to a location with clues from a location with none, setting yourself up to Duke on in there and bring the hammer down.
So, if it's synergy you want, and perhaps something slightly off the wall, then Alice, Pete and Duke are ready to protect and serve.