Akali jungle is how I play her. I take red candy (elixir) and 1 hp pot. Go to double golem. Attack one, let it hit you, take elixir and health pot. Smite the first one you attacked, kill off 2nd. I use Smite/Ignite, I then go to wraths, ignite the blue one and kill it. Also taking the ignite mastery gives you your 2nd passive. That's the fastest way I've found to jungle with her. Usually someone in a lane needs to go back, so often I grab a free level out of that also when the chance occurs.
I build Gunblade first, with swiftness or mobility boots depending. Speed is Akali's best friend. After Gunblade I get Crystalized Scepter. Then usually Guinsoo's Rageblade. There's a lot of ways to jungle her but I've found this the most effective. And a proper runepage setup is very important.