I am bored. مل (malla) is Arabic for 'he became bored'. ملیت is not how you would say it in Standard Arabic, though; that would be مللت (malaltu). The sentence you provided is in Egyptian Arabic and translates to: I am sick of how much I have sacrificed and how I've never tasted bliss.

بالعامية معناه الملل: الطفش والزهج بالفصحى الملل الشعور بالضجر

I have been studying Arabic for several years, is this sentence in some local Arabic?

It means: I bore..