We present numerical results concerning the combustion that occurs in a three-plan jet system, which represents the two-dimensional version of a coflow gaseous injector of hydrogen and oxygen. The study focuses on the hydrodynamic effects--damped by combustion--that affect the high-speed jets at the entrance of a combustion chamber. The concerned parameters mainly involve the inlet flow velocities in a range where flame attachment occurs. The results confirm the classical idea according to which mixing-layer combustion damps shear-layer instabilities. Moreover, steady or unsteady solutions can be exhibited for the same set of parameters. For various ratios of density and inlet velocity (established between oxygen and hydrogen jets), we study the coflow dynamics (under combustion), which can be interpreted in terms of momentum flux ratio J. When increasing J, the dynamics become more and more complex, exhibiting large amplitude flapping, which produces the widening of time-averaged temperature field. For high J values, the dense oxygen jet is rapidly stripped and takes the same pattern as the liquid core observed in LOx injectors, with a dependence close to the Jm1/2 law measured for dense core length (albeit presently studied Reynolds numbers are one decade less).