Spinning the tire is horsepower and friction limited. A 1000 hp motorcycle is going to spin the tire any time the rider wants to dial it at any speed.
An RS125 can spin the tire right off the start, but at some point the power to the rear wheel through gear changes and aero drag will limit the engine to less power than is available to spin the tire. The other guy with an identical bike that weighs 10 pounds more/less than you can't give you valid info either. I guess you will find out! I doubt at 138 mph that you will have tire problems.
You didn't mention the track. Asphalt, alkaline lake beds and salt have very different coefficient of friction, and they all change with atmospheric conditions.
Tire chunking happens when the force on the tire exceeds the structural strength of the tire. Spinning the tire heats it up. Side wall flexing is the majority of the heat the tire sees. I've watched overloaded test tires go from ambient to 160 F in 30 seconds at the sidewall. Centrifugal force increases with speed and at some point the tire will come apart even if it isnt in contact with anything. The combination of load, heat, speed and inflation pressure determines when the tire will come apart.
At 200 mph the tire is loading and unloading at the contact patch 50 times per second. The DOT speed ratings have a safety factor, but with non-DOT racing tires it may be difficult to determine what the maximum speed would be.