Flame particles (FP) are massless, virtual particles which follow material points on the flame surface. This work presents a tracking algorithm for FPs which utilizes barycentric coordinates. The methodology can be used with any cell shape in the computational mesh and allows computationally fast spatial interpolation as well as efficient determination of the intersection of FP trajectories with iso-surfaces. In contrast to previous flame particle tracking (FPT) approaches, the code is fully parallelized and can therefore be used in-situ during the simulation. It also includes fully parallelized computation of flame consumption speed by integrating reaction rates along a line normal to the flame surface at each FP position. Direct numerical simulations of laminar pulsating premixed hydrogen–air Bunsen flames serve as validation cases and showcase the added value of tracking material points for studying local flame dynamics. Exciting the inlet flow harmonically with frequencies equal to the inverse flame time scale leads to a pulsating mode where the flame front is corrugated. Ten times higher frequencies nearly resemble the steady state solution. The FPs are seeded along the flame surface and are used to track the unsteady diffusive, convective and chemical contributions at arbitrary points on the flame front over time. Their trajectories reveal a phase shift between the unsteady flame stretch rate and local flame speed of the order of 0.1 flame time scales for rich hydrogen flames. This is caused by a time delay between straining and stretch due to curvature. The reason is that diffusive processes follow the time signal of curvature while chemical processes are most strongly affected by the straining rate, which dominates the high Lewis number hydrogen flames investigated. This time history effect may help to explain the large scattering in the correlation of local flame speed with flame stretch found in turbulent flames.