Ok, let's break this one down... The sheer lack of understanding and respect for the English language spreading like a stupid wildfire is making me sick.
1) to jack something is slang for "to steal."
2) swag is common slang for "stuff we all get." Generally speaking, the big bag of random and mostly useless crap you get at a convention of sorts.
Therefore, "jack my swag" quite literally means to "steal my bag of swag (stuff we all get)"
Though, the unfortunate truth of the matter is, this is what people who don't think about what words coming out of their mouths think means "jack my swagger" or to "steal my style".
For example, this might be used at a comic book convention and some fat sweat kid might exclaim "Hey that guy just jacked my swag!" Or some 13 year old girl with a clear misunderstanding of how the English language works and doesn't understand that you don't just abbreviate words at will, might say "jack my swag" as part of her auto-tuned music video expressing her distaste of other people wearing the same jeans. Clearly her strong sense of entitlement under her rich daddy umbrella is completely warranted and supported.