Zap may have the strongest AD scaling of any ability in game. Use it EVERY time you land Flame Chompers. Also, use it to check brush- it's got a low CD and reveals anyone it hits.
Flame Chompers is not a very strong escape- use it to zone enemies in teamfights and prevent them from escaping.
Build an Essence Reaver (Note: Jinks is the only champ who I would ever build this item on.). It allows her to recoup the cost of her rockets by farming. This is an incredible help with your poke, since it allows you to not worry so much about mana costs, which are a bit high for her. You can sell this once you have a full build, since she has great mana and mana regen scaling per level.
Your ult is an execute. Use it to clean up after teamfights, or kill single enemies in other lanes after they try to escape their lane opponent.
Skill leveling priority- Get a point in Q first. Then, a point in W, another in Q, then 1 in E. Finish leveling W, then max Q.
Exceptions- Against Cait/Ashe/Kog, 2 points in W, then max Q.
Only commit if you can get a kill. However, don't worry too much about escapes- your passive gives you a ton of movement speed so you can escape most of the time.
Good luck on Summoner's Rift!