We carried out a computational study of propagation speeds ofreaction-diffusion-advection fronts in three dimensional (3D) cellular andArnold-Beltrami-Childress (ABC) flows with Kolmogorov-Petrovsky-Piskunov(KPP)nonlinearity. The variational principle of front speeds reduces the problem to a principaleigenvalue calculation. An adaptive streamline diffusion finite element method is used inthe advection dominated regime. Numerical results showed that the front speeds areenhanced in cellular flows according to sublinear power lawO(δp),p ≈ 0.13, δ the flow intensity. In ABC flows however,the enhancement is O(δ) which can be attributed to thepresence of principal vortex tubes in the streamlines. Poincaré sections are used tovisualize and quantify the chaotic fractions of ABC flows in the phase space. The effectof chaotic streamlines of ABC flows on front speeds is studied by varying the threeparameters (a,b,c) of the ABC flows. Speed enhancement alongx direction is reduced as b (the parameter controlingthe flow variation along x) increases at fixed(a,c) > 0, more rapidly as the corresponding ABC streamlines becomemore chaotic.