1 Uncle Owen: Luke! Pack your bags! We’re leaving Tatooine!
2 Luke: Why, Uncle Owen? Is it to flee the Empire?!
3 Uncle Owen: Nah. I’m jack of trying to run a moisture farm on a desert world.
4 Uncle Owen: We’re moving to Kamino. I hear the harvests are much bigger there.

I figure if Owen Lars is the son of Cliegg Lars, who was clearly Australian, then it's perfectly plausible for him to use "jack" in this way.

I note with interest that even though the word "jack" has around 40 different meanings in English, according to Wiktionary Australia is the only place that uses it as an adjective. If you're too lazy to click the link, it means "sick and tired" or "fed up". Grammatically, it's always followed by the preposition "of", never "with". You're always "jack of" something, not "jack with" it.