In flame tests, ions are excited thermally.  These excited states then relax to the ground state with emission of a photon.  The energy of the excited state(s) and associated emitted photon is characteristic of the element.  The nature of the excited and ground states depends only on the element. Ordinarily, there are no bonds to be broken, and molecular orbital theory is not applicable.  The emission spectrum observed in flame test is also the basis of  flame emission spectroscopy, atomic emission spectroscopy, and flame photometry.