as a mage, ahri is played as a mid, usually getting to level 18 is the goal to acheive with ahri so you can have max spell damage output as well as your AP. staying in your lane can get the the most Xp and with occasional arousal to your enemy in your lane, you can Xp block and hit level 18 before everyone else.
Depends in what the other players are like. if they start building up on magic penetration,take the void staff, otherwise take will of the ages for spell vamp replacing Dorans ring). Morellos Evil tome for cooldown reductions ( which are really good help in late game). Rod or the ages and Rylais Crystal Sceptre for Health and Regerations. mana isn't a problem late game as you can come in and out of battle with enough mana to fight.
taking flash to escape rough situations and in case low health to flash to a turret really helps since your only in mid by your self. even though spirit rush can help as an escape tool, flash is really good early, mid and late game. clarity is good early and sometimes mid if your low on mana. it is good for avoiding recall so you can stay in lane and keep gaining xp and gold.
i take orb of deception to acheive max damage in and out to not only champions but alos minions. also since its the best spell for Souleater, taking out minion waves with this spell with give to the maximum health from souleater. occasionally taking in charm for the duration, since it is a good escape tool as well as a to bring enemies closer to you. fox fire does the most damage when maxed and have massive amounts of Ap, taking out about 500-700 when level 18 with appropiate items.