you have a pressure seal pressing against the rim caused by the tire which is shielding your tube, and a rim strip under that to give more protection, if the chrome is flaking, any chrome that could cause the tube to pop would be already inside the rim, with little to no ware in that section of the rim, on the other side of the tire, a high pressure seal is pushing against the chrome keeping it in place and creating a seal.....
Nothing will happen to your tube, Collin's just Trolling you...
try this, Get some chrome polish, polish up your rims, and get some high gloss clear coat rustoleum and give it a few coats of clear. should help minimize the flaking, and keep your rims from starting to rust.