An "amp neck" refers to an individual to who tends to ampilify drama, personal achievements, personal abilities, or other's flaws. The process of becoming an "amp neck" involves amping or amplifying the maginitude of any given situation to the point where it is either annoying, false, or just bullshit. The "neck" part of "amp neck" is similar to the usage of "neck" in red neck. It is simply additional and sounds degrading of the individual being described.
Kyle is being an amp neck by talking shit about everyone and how much better he is than us.