broke several laws

He did no such thing. The "illegal gun across state lines" thing was straight up fake news (gun was always stored in Wisconsin), the curfew violation charge was thrown out because it was found to be unconstitutional, the underage weapon possession charge was thrown out because possession of a rifle or shotgun (unless it's a short-barrel) is actually legal in wisconsin for 16-17 year olds, and the other 5 charges were all homicide, attempted homicide, and a reckless endangerment charge because the first guy he shot had someone else ~30 feet behind him in the line of fire.

All of the remaining charges that actually made it to the jury deliberation phase of the trial have self-defense as an affirmative defense, which is why the jury came back as not guilty on all counts. Everything that happened that night is on video, and Kyle never provoked anyone. Hell, the guy that jumped him initially did so in part because Kyle had put out a fire he started earlier, and jumped him when he was trying to put out a different fire.

This is kind of an aside because he couldn't have known this at the time he shot them, but I think it's rather telling that all 3 of the people that attacked him that night had notable criminal records. One was a convicted child rapist that had sexually abused 5 boys between the ages of 9 and 11, another had multiple domestic violence convictions for hitting his grandma, and the third had burglary and DUI convictions, and unlike Kyle was illegally carrying that night, because you need a permit to carry concealed, his permit had been either revoked or had expired (still not clear on this), but he was carrying a pistol concealed anyways.

I don't think what happened that night was a good thing, but I think it's inaccurate to say he "got away with it". You may not like the laws, but everything he did was legal.