Laser-induced breakdown is a versatile means of depositing energy in a fluid and a promising alternative to conventional electrode-spark ignition for combustion systems. Using numerical simulations we analyze the flow dynamics following the laser pulse and show that it is sensitive to even subtle alterations in the plasma kernel, which lead to qualitative changes in the flow pattern and ejections of hot gas from the laser focal region. This sensitivity is leveraged in a dual-pulse configuration, in which the timing and positioning of the pulses can be controlled to enhance dispersal of hot gas and increase the burning rate of nascent flames. In an inhomogeneous mixture, it is further shown that the rapid plasma expansion can produce ignition-suppressing flow so pronounced in some cases that ignition fails. The dependence of these hydrodynamics on electron recombination and diffusion is also assessed.