Timing Vault gives it more utility than just a crowd control effect. Let her passive trigger, follow with Vault and then another autoattack to deal a quick burst of damage.
Opening with Vault will put her passive on cooldown, potentially lowering your damage output.
Pay attention to where you are positioned when using Vault. Be aware of the surrounding walls so you don't pin your self in a corner or accidentally flee from a fight.
Vault can be used to turret dive effectively mid-late game. wait for an enemy to become marked, attack it, Vault, hit them again and run.
Be careful using this tactic against someone with a stun or strong slow.
Quinn does not have an on-command, active steroid like other carries, so putting points into Heightened Senses faster helps her get more out of her passive steroid in a shorter period of time.
Blinding Assault is a collision linear skillshot that blinds and deals damage around the first enemy hit. This means enemy minions can block the damage (and more importantly, the blind effect) unless they are close to the enemy champion.
Using Blinding Assault to momentarily interrupt an enemy's damage output can give you or a teammate a split second of relative safety to deal some burst damage. Try noting when your target has used either their nuke or their crowd control effect before going for a "blind and burst" combo.
Tag Team is best used to get around the map, such as split pushing or chasing/fleeing from an enemy.
Activating Tag Team is also good when wanting to hunt down and assassinate an enemy champion with low health especially with the damage from Skystrike.
While in the jungle or near jungle camps you can use Heightened Senses and Vault to dash through walls by targeting a neutral monster.
Vault is especially useful for escaping across walls by jumping off a neutral monster or enemy champion, though is not reliable and needs practice to master.
Harrier marks are visible by the enemy team, and may make them play safer for the duration.
Tag Team can be used a couple of ways. It can be used to escape, to increase her damage output, or to roam to other lanes. however, it disables Harrier, so on the long run it not may only reduce your range, but your damage output as well.
Tag Team gives bonus movement speed even if you are in combat, but the movement speed is much higher while not. This, used with the surprisingly long duration, may allow Quinn to reengage into the fights several times, or kite with a huge effinecy.
The Black Cleaver works especially well on Quinn. Not only will it increase her damage output but also increase her survivability and provide CDR allowing her to make better use of her skills.
Berserker's Greaves are not the only useful boots on Quinn. Since she has short range and gets into melee range with her ultimate, Mercury's Treads may be a good idea to reduce CC effects.
Although the Zephyr is not normally built on ADC it can be a useful item on Quinn & Valor. Apart from the Attack Speed bonus and Attack Damage, the tenacity and movement speed bonuses help with her mobility making better use of Tag Team as well as CDR, letting her use her skills more often.
As with all carries, rushing an Infinity Edge is a good choice and building The Bloodthirster (or Sanguine Blade) as with all carries is a strong choice. Not only will it increase her damage output but also giver her more survivability and durability
Statikk Shiv is especially good on Quinn as it gains stacks from Vault, and may stack quite fast with her increased attack and movement speed. It also increases her burst potential.
For defensive items, Frozen Mallet can be considered as an option, as it not only increases her health, but her attack damage, and gives her unmatched kiting potential with Vault and the flat movement speed bonus of Heightened Senses.
Quinn can also be played as a fairly strong toplaner. When playing her sololane, remember to buy some early tank items such as Giant's Belt, Negatron Cloak or Chain Vest.
The slow from Vault does fade over time, making tenacity more useful in countering one of her two crowd control abilities.
Quinn lacks hard crowd control abilities, and as such has little in the way of stopping a more durable champion that does good damage through spells.
Aside from Tag Team, Quinn has few strong escape or disengage abilities. Additionally, as Valor her Vault no longer has the effect of repositioning her. Forcing Quinn into a bad position can keep her presence low.
Keep in mind that Quinn has a higher burst potential than most or the carries.
Vault can be stopped mid-air, interrupting her combo, and leaving her out of position.
You can see an enemy Quinn'sHarrier marks. Use this to lure her out of position.