I've spent the past day or so watching some games with Jhin, and I've even gotten in a couple of games playing as Vega with a gun. After my journey across the realms of the PBE this is what I've dug up and have to offer.
Jhin's Niche
Sniper caster-carry hybrid with long-range cleanup capability. A literal marksman.
Pros
Huge early-game trades
Good snowballer
Safe farming and lane harass
Generous Attack Damage scalings on all abilities
No qualms with farming under tower
Good for a solo lane or duo
Easy champion to pick up
Cons
Susceptible to falling off late
Base 325 movement speed
Squishy without lifesteal
Very little self-peel
Bad duelist past level 6
Jhin's Damage
It's no secret that, being a caster/carry combo, Jhin deals largely physical damage. He indeed deals high-scaling physical damage on Dancing Grenade (Q), Deadly Flourish (W) and Curtain Call (ult). Both his passive fourth hit and all hits of Curtain Call scale with the target's missing Health.
Lotus Traps (E), though, do magic damage that scales generously with total AD, making backline snipes exceedingly rewarding in the late game.
Deadly Flourish
This is Jhin's W spell and it is deceptively good. It's a 2500 range ability that hits through minions and snares if your target has recently taken damage from an ally, and gives you a speed boost if the snare lands successfully. It will generally see more use in a duo lane than a solo lane, since ally damage procs it, but at the mid to late levels it sets up quick clearing of a marching wave via Dancing Grenade. Always be mindful of where you use it from, however, as with 2500 range it can easily give away your position via ward.
Jhin, Jhin, Jhin of the Jungle
Watch out for that creep! ...uh, if you didn't catch that 90's Disney reference, pay it no mind. Anyway, Jhin in all likelihood won't be considered a viable jungler by any stretch, as a lack of sustain and mobility hurts him dearly in early jungling when he otherwise would actually have competent clear speed between his spells and crit autos. One notable thing though, is that he can gank...without actually ganking. Aggressive laners will love having the support of a long-range snare from well out of ward range thanks to Deadly Flourish, and the potential threat of the equally long-range executes, which are devastating with lockdown applied from a laner. Even so, I don't recommend trying this without at least running it through a bot game or two first.
Power spike
Jhin can be a tremendous early-game force, even for a ranged AD. Dancing Grenade's damage is amped up with each unit it kills as it bounces, so when it finally boinks an enemy champion, they can really feel the pain. When Jhin's abilities are on cooldown, the threat of his crit auto can discourage trades, and vice versa. As mentioned before, if facing an enemy like Graves or Malzahar who is going to shove the wave in, not a problem. Jhin's early damage can make life absolute hell for melee champs in lane, such as Talon, who will constantly get whacked with everything Jhin has and may be driven straight out of lane early on. Said damage also makes farming under tower deceptively easy; however, he doesn't have much of an answer in this situation vs long range utility mages like Orianna and Lux, so it's up to him to assert lane dominance...which he really won't have much of a problem doing with his early-game power.
Example build 1
Wanna give Jhin a run soon? Try doing this build...
Infinity Edge
Rapid Firecannon
Ionian Boots of Lucidity
Death's Dance
Lord von Dominik's Regards
Defensive item (Guardian Angel, Zhonya's Hourglass, Mercurial Scimitar, etc.)
Infinity Edge and Rapid Firecannon are pretty much no-brainers. The synergy between Jhin's kit and these two items is beautiful, especially if Jhin can proc Rapid Firecannon with the fourth shot. Ionian Boots of Lucidity has been my preferred choice for boots, but Jhin doesn't do too badly with Berserker's Greaves as that does tack a little more onto his lackluster mobility for 300 gold.
The optimal choice for third item has made for a very heated debate on the PBE chats; Essence Reaver for some, The Bloodthirster for some others, but for me and a few other peeps, Death's Dance. This item can give you so much health back when clearing waves and camps that it's nuts, and you can keep chucking out Grenades and Deadly Flourishes while having an easier time surviving thanks to its other passive.
As for the last item, go with what you think you need, but a lot of people have been theorizing that the benefits of a sixth offensive item outweigh the need for a defensive one. Personally, I disagree given how immobile Jhin can be, but hey. We'll see in time if it really is worth sacrificing survivability.
Jhin's been quite a bit of fun so far! Looking forward to getting more time to play as him this weekend.