They play musical chairs once I'm on that pedestal
Before one is hung he is usually standing on a chair or pedestal. In the game of musical chairs everyone fights for a chair, and after each round a chair is removed. When Kendrick say “they play musical chairs once I’m on that pedestal” he means once the government has had enough of him, or whoever disagrees with his views, he will be tied to a rope by his neck, and the chair/pedestal he is on will be removed.
Also the KKK were known for lynching African Americans who tried to express their views, or the ones who were in the government.
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