Several misconceptions in this question.
1. Kinetic energy is a property of particle in given coordinate system. Perform the following experiment: imagine a coordinate system moving with 99.9999991% speed of light with respect to you. In that coordinate system you are moving with 99.9999991% speed of light and your kinetic energy is enormous. However, while performing the experiment you will notice no change in your body or your surroundings, and performing this imagination is entirely safe.
2. Kinetic energy is not internal energy of an object. Consider the following examples:
a) You throw a piece of ice. You increase its kinetic energy, but nothing bad happens to it while its flying.
b) A flying piece ice hits the ground. It may break, because its kinetic energy transforms into other forms of energy, like mechanical waves or heat.
c) You put a piece of ice on a stove and turn on heating. Soon the ice will melt. The piece doesn't move, you don't increase its kinetic energy. You rather increase its thermal energy. Thermal energy is related to kinetic energy of individual water molecules, but total kinetic energy of the whole piece of ice remains 0.
The fact that a proton is moving fast doesn't change anything about it. The quarks and gluons forming a quickly moving proton behave the same as those in a stationary one. Only if our proton collides with something, e.g. 815
with another proton moving in the opposite direction, their kinetic energies can be transformed into something else, e.g. breaking them and forming new particles.
A fast moving proton is something quite different than what's called excited proton or more often excited nucleon which has elevated internal energy, in form of angular momentum and spin configuration. Excited nucleons can be created in high energy collisions, such as those in LHC, and are very unstable; after very short time they release their extra energy (in form of new particles) and decay back to "regular" proton or neutron state.
1. Several people mentioned decays. I think this is not what you asked about. You speak about disintegration of a proton due to its large internal energy, e.g. similarly to breaking or melting piece of ice. The only way we have to increase internal energy is by colliding the proton with something else. That's something completely different from spontaneous decay.
Some particles are unstable and decay into other particles after some time. Decay of proton is theorized, however it hasn't been discovered experimentally. Therefore proton is either stable, or its lifetime is extremely long.
Particle decays are actually affected by their movement, due to time dilation. Time passes slower for a moving object. E.g. muons produced by interactions of cosmic rays high in the atmosphere reach the ground, despite their mean lifetime of 2.2µs multiplied by the maximum speed they may have, speed of light is only 660m. So if proton could actually decay, it would even less likely do so if it moved with relativistic speed in an accelerator. 781