This is just an idea I had the other day. With Janna's abilities and stats, a hybrid build isn't totally out of the question. Granted they lean more towards an AP champ but this build is built around that. I don't expect this build to become ranked game worthy but if you feeling like messing around with a really fun champion then feel free to try this out.

Great Mark of Insight- The majority of the damage you will be doing will be magic damage (spells and Lichbane) so it makes sense to get magic penetration.

Greater Seal of Alacrity- This will synergize well with your E-ability. More attack speed = more utilization of shield/damage increase

Greater Glyph of Force- More ability power means better more damage from spells and Lichbane, more shield from Eye of the Storm and more healing from Monsoon

Greater Quintessence of Fortitude- 78 more health = more survivability early game.

I go with a 21/9/0 tree for Janna, Avoiding the critical strike damage talent in offense as we don't plan on crit-ing to often. I choose defense for the last 9 because the extra armor and magic resist never hurt anyone (especially not you) and Strength of Spirit stacks amazingly with all of the mana you get

This play style requires a lot of mana and cdr as you want to be able to proc Lichbane as often as possible. So Archangel's Staff and Nashor's tooth are perfect. They give you the attack speed, ability power, cdr and, most importantly, the mana. With a Lichbane proc, You can hit someone for 400 easily (basic Mr is taken into account here) and that doesn't include the spell you cast to get the proc. Malady and Nashor's Tooth just stacks extremely well with your E-ability as well as shredding their MR and then a Rabadon' Deathcap to give you a huge boost in ability power.

I prefer to start a fight off with Howling Gale, auto attack, and then Zephyr. This can maximize the damage you do to them before they can get to you (if they are melee). Once they start attacking you shield yourself to reduce damage taken as well as giving you another Lichbane proc (which will stack with the damage buff you get from the shield). If you are low on health at this point knock them back and heal with Monsoon (try to knock them back towards your tower). If not just auto attack until your spells come off cool down. That's the great thing about hybrid builds. Your abilities don't become useless like in an AD build nor do you have to wait for your spells to do damage. Make sure that you aren't casting all of your spells in a short amount of time. Lichbane has a 2 sec cooldown so cast a spell and then auto attack three before casting another (one to get rid of the proc and the others for the cooldown). This is very important as Lichbane more than triples the damage your auto attacks do. Another tip is that if you cast Howling Gale and then immediately auto attack and then release the whirlwind right before it is meant to go off you can get another Lichbane proc.

I choose flash/teleport because it is a very solid setup. You cant go wrong with it. You could trade teleport out for ignite or exhaust. It's all about personal preference although I am a firm believer in flash for every champion.

I just want to reiterate: This build is not going to win advanced normal or ranked games. This build is just a guide to people who are bored and want to try something new. This build is all about a consistent stream of damage coming from auto attacks and spells. Bursting is possible but it doesn't output as much damage as when you pace yourself. Good luck and have fun. :)

Tips and criticism welcome just try to be polite