The composition of relativistic gamma-ray burst (GRB) jets and their emission mechanisms are still debated, and they could be matter or magnetically dominated. One way to distinguish these mechanisms arises because a Poynting flux dominated jet may produce low-frequency radio emission during the energetic prompt phase, through magnetic reconnection at the shock front. We present a search for radio emission coincident with three GRB X-ray flares with the LOw Frequency ARray (LOFAR), in a rapid response mode follow-up of long GRB 210112A (at z~2) with a 2 hour duration, where our observations began 511 seconds after the initial swift-BAT trigger. Using timesliced imaging at 120-168 MHz, we obtain upper limits at 3 sigma confidence of 42 mJy averaging over 320 second snapshot images, and 87 mJy averaging over 60 second snapshot images. LOFAR's fast response time means that all three potential radio counterparts to X-ray flares are observable after accounting for dispersion at the estimated source redshift. Furthermore, the radio pulse in the magnetic wind model was expected to be detectable at our observing frequency and flux density limits which allows us to disfavour a region of parameter space for this GRB. However, we note that stricter constraints on redshift and the fraction of energy in the magnetic field are required to further test jet characteristics across the GRB population.