Flash
Flash on Kennen is extremely Important as it can help you counter champions who displace you when you are attempting to Lightning Rush into the teamfight. It is also used to escape from annoying junglers such as Jarvan who can lock you down. It will also help you get a better position during teamfights. Never go into a game without Flash on Kennen.

Ignite
Ignite gives your more burst potential and makes the enemy laner wary of your damage. It can be used to kill of stragglers or to disable champions which are reliant on spellvamp/lifesteal. Ignite is the recommended spell I would use for Solo Queue.

Teleport
Teleport can be taken to apply global pressure during all parts of the game. During the early game, any aggression on the bot side of the jungle can easily be followed up by a teleport from Top lane to turn the tides. During late game, you can use Teleport to your advantage by splitpushing and forcing an enemy to defend against you, then teleporting to your teammates for an easy 5v4. However, you will lose a lot of kill potential in your lane, and higher level opponents will take advantage of your Summoner Spell choices. Teleport is a decent Summoner spell if you feel that you are unable to win your lane and would prefer to help other lanes.

The Laning Phase
Kennen is an extremely strong lane bully with almost no lane counters. With his dual form of harassment, he will be able to whittle down any opponent and finish them off with a well timed ult. Also, it is near impossible to gank a properly played Kennen as Lightning Rush is effectively a mini Aegis worth of Stats combined with Ghost, making you a tanky and highly mobile yordle. Always remember to apply your Mark of Storm correctly to prevent overlaying of cc.

Harassing
Kennen has very good harass in lane. He is also very annoying to lane against especially as a melee opponent. Every time the enemy attempts to cs, auto attack them once or twice. If they are greedy enough to try and farm a ranged minion, go crazy and apply your 3 mark of the storm to chunk them down. You should always have a huge cs lead against most melee laners as they will not be able to farm without losing at least 100 hp every time they attempt to. Against ranged opponents, you will not be able to exert as much pressure on them. However, the opponent will be unable to touch you as well. If you see them attempting to land a spell on you, cast Lightning Rush backwards, throw out a Thundering Shuriken and an Electrical Surge to chunk her down. This will usually discourage opponents from harassing you any further.

Using your stuns correctly
Kennen's mark of the storms is his core mechanic. Always take note that Kennen's stuns have diminishing returns if layered immediately after each other. Also remember that it take 3 marks to trigger a stun, so missing a crucial autoattack or Q might be the difference between life or death. Kennen will also run out of energy quickly if you keep spamming your abilities. Therefore it is wise to always keep track of your marks and plan ahead to trigger them to make the most out of your abilities.

Team Fight
During a teamfight, Kennen's role is to stun lock the enemy team while his team cleans up. If you manage to find yourself behind and do not have a Zhonya's, it is more beneficial if you stick with your carries and act as an AOE peel for them. After blowing your ultimate, you should be chasing off opponents with low health, or attempt to peel for your carries with more mini stuns.

Solo Laning
When you are laning your goal is to keep range advantage on your opponent and harras from safety while getting a decent minion advantage. Constantly shoving the lane to your enemies turret while having proper wards can put out a lot of pressure on the enemy, and will allow your team to gain free objectives if the jungler decides to waste his time to visit your lane.