The build includes appropriate items to buy. (Personally, I wouldn't build Archangel's but that's just me. Rod of Ages provides HP, Void Staff could replace Archangel's instead. I also don't think she can effectively charge up the mana better than someone, say Ryze. The ~900 gold could help you get a Revolver earlier on, should you want to force enemies out of lane with constant trades. ) I find your runes, skilling order and masteries to be ideal. However, I feel like the formatting could be better, and it could include more about what Ahri's playstyle is throughout the game.
Your match-ups should include more champions, and I'm questionable about some match-ups that you name hard.
Just stay away from Fiddlesticks and he can't Drain/Terrify you. If he uses Dark Wind to harass, heal it back up. Your charm cancels his Drain channel if you can land it. He also pushes somewhat slow (I don't know how big the Dark Wind buff is, but I'm pretty confident Ahri can out-push him.
Ryze has short range spells, and is squishy early on. Charm can disable him for a short while, maybe when he's just hit a Rune Prison on you.
Xerath's Arcanopulse has a relatively long cooldown, having 5 seconds only at max rank. If he misses that, you can punish him hard. Mage Chains won't be able stun in time, unless he's level 6 and is willing to use his ultimate/has it up.

Thanks a lot! I have both those items in my alternate item chapter ^^ it all depends on what the enemy team builds, but on average games the build I put works the best from testing.

The guide is aesthetically great. No problems with how it looks, nor it's layout.

However, your items are iffy. I'd suggest not buying the RoA and replacing it with Zhonyas.
Also, include an early tear for your archangels.

You can also buy RoA first since mid game is largely about survivability and sustain. In my opinion, you don't really need it.

Another thing is that you have no Magic Pen/Reduction hence late game you'll fall off, and even from mid game, any magic resist will hurt hard. A void staff is pretty strong, and essentially necessary for Ahri. I'd get rid of the archangels for it, or the RoA.

Apart from that, +1 from me, well written.