Because Ahri already has 3 dashes with Spirit Rush you might think that flash would be less necessary, but I cannot think of any situation where I would not take flash. It is by far the most useful Summoner Spell in the game. The reason that Flash is so good on practically everyone is because it acts as a 'get out of jail free card'. There are so many sticky situations that Flash can get you out of, whether it is being ganked, being trapped by a wall or needing to get away from a Champion or tower as quickly as possible. Flash is also great for offensive uses, it enables you to chase someone down over a wall or to get close enough to use an ability on them. Flash can also be used to dodge abilities such as Final Spark, Mega Inferno Bomb and Rite of the Arcane. I recommend that you always take Flash on Ahri, there is no question about it.

The second most important Summoner Spell for Ahri is Ignite. Ignite is the perfect spell for an Assassin or high damage Mage like Ahri due to the raw damage that it brings to the table. Ignite is true damage which means that it cuts straight through any resistances the target may have. It is a great extra ability to finish enemies off with and generally help win a fight. It also increases Ahri's ability to instantly kill someone as ignite does do a fair amount of damage. A level 6 Ignite does 170 damage, level 11 it does 270, and level 16 it does 370. Mid-Late-Game ignites can deal quite a large chunk of a Champions health bar. Another great benefit to Ignite is that it straight up halves all healing of the Ignited target, so if you Ignite someone like Nidalee, her Primal Surge will only heal for 50% of its total amount which can be quite huge in a fight.

Exhaust is probably the only serious contender for Ignite as it can greatly help in matchups where your opponent is likely to all in you and burst you down, such as Zed, Yasuo or an AP matchup like LeBlanc. Exhaust is much easier to use against a melee Champion though because they will always be in range for you to use it, vs a ranged AP Champion you might not be able to get it off in time. The only time I might run Exhaust would be if I was against either Zed, Yasuo or Talon. Even then I would still likely take Ignite instead because you need it for kill pressure.

Teleport could be useful when laning vs a Twisted Fate to answer his ultimate with your own TP but it's honestly not that good. Being mid lane you are quite close to every part of the map, and being Ahri it won't take long to get from one point to another to assist your team or catch someone out. For the odd case that you might be Ahri Top, TP would probably be a good replacement for Ignite but for mid lane Ahri I would not use Teleport.

Rune Page 1 (Standard AP)

This Rune page should look fairly normal for a Mid laner and it is the standard Rune Page I use when playing Ahri in a comfortable or favourable matchup. Some examples of Champions that this page would be used against are: Ziggs, Nidalee, Lissandra, Karthus and Twisted Fate
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Rune Page 2 (Armor)

This rune page is the go-to page for when you have an AD matchup as Ahri. So if you are facing a Zed, Yasuo, Talon, or any other physical damage dealer you MUST take a page that has armor or else they will shred you. The only difference between this page and the standard page is the armor.
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Rune Page 3 (Move Speed + CDR)

Here's where we get to the interesting Rune Page. The Movement Speed Cooldown Reduction page. Now I know a lot of you might be thinking this Rune Page looks crazy and there is no AP so how can it work. Fear not, I will explain it heavily. Movespeed Runes are honestly some of the best Runes you can use on Ahri, they synergize very well with her being a heavy roam Champion. It also helps her out a great deal in matchups that require a lot of dodging such as Syndra, Ziggs, Lux, Morgana, Cassiopeia and Xerath. I will always take this page when I know I am against a Champion that has a lot of skill shots because movespeed Quints paired with a Boots start makes it extremely easy to dodge almost any projectile. They also make roaming faster and they help tremendously when getting ganked, especially when it's a Jungler such as [[udyr], because he has no gap closer other than raw speed.
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Rune Page 4 (Magic Resist)

his is the defensive Magic Resist page. It is basically the page you will almost have to use when facing heavy AP Burst. Great examples of Champions that you would use this page against would be Annie, Syndra, LeBlanc, and Veigar. So basically this is the page you would use against Ahri's hard counters.