The present experiments focused on the response of burning gaseous fuel jets to prescribed transverse acoustic excitation as a means of exploring the coupling of reactive, acoustic, and flow processes relevant to combustion instabilities. Single reactive methane microjets were exposed to transverse resonant standing wave disturbances within an acoustic waveguide for which a range of amplitudes of excitation were applied. Temporal flame response to acoustic excitation was studied via simultaneous phase-locked OH* chemiluminescence and visible imaging, and additionally via high speed, temporally resolved visible imaging. Quantification of flame dynamics was achieved for phase-locked data via the Rayleigh and temporal flame distortion measurements, and for time-resolved data via proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). Characteristic signatures associated with various types of flame response were identified, including weakly oscillatory combustion, full-scale flame coupling and lock-in to excitation, and multi-mode flame dynamics preceding flame extinction. It was found that modal decomposition of flame dynamics via POD and DMD analysis revealed important additional dynamical features and signatures in metrics characteristic of transitions in the flame-acoustic coupling.