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Solar flares are intense bursts of electromagnetic radiation accompanied by energetic particles and hard X-rays. They occur when magnetic flux loops erupt in the solar atmosphere. Solar observations detect energetic particles and hard X-rays but cannot reveal the generating mechanism because the particle acceleration happens at a scale smaller than the observation resolution. Thus, details of the cross-scale physics that explain the generation of energetic particles and hard X-rays remain a mystery. Here, we present observations from a laboratory experiment that simulates solar coronal loop physics. Transient, localized 7.6-keV X-ray bursts and a several-kilovolt voltage spike are observed in braided magnetic flux ropes of a 2-eV plasma when the braid strand radius is choked down to be at the kinetic scale by either magnetohydrodynamic (MHD) kink or magnetic Rayleigh–Taylor instabilities. This sequence of observations reveals a cross-scale coupling from MHD to non-MHD physics that is likely responsible for generating solar energetic particles and X-ray bursts. All the essential components of this mechanism have been separately observed in the solar corona.