The inclusive J/ψ elliptic (v₂) and triangular (v₃) flow coefficients measured at forward rapidity (2.5 < y < 4) and the v₂ measured at midrapidity (|y| < 0.9) in Pb-Pb collisions at sNN = 5.02 TeV using the ALICE detector at the LHC are reported. The entire Pb-Pb data sample collected during Run 2 is employed, amounting to an integrated luminosity of 750 μb⁻¹ at forward rapidity and 93 μb⁻¹ at midrapidity. The results are obtained using the scalar product method and are reported as a function of transverse momentum p_T and collision centrality. At midrapidity, the J/ψ v₂ is in agreement with the forward rapidity measurement. The centrality averaged results indicate a positive J/ψ v₃ with a significance of more than 5σ at forward rapidity in the p_T range 2 < p_T< 5 GeV/c. The forward rapidity v₂, v₃, and v₃/v₂ results at low and intermediate p_T (p_T ≲ 8 GeV/c) exhibit a mass hierarchy when compared to pions and D mesons, while converging into a species-independent curve at higher p_T. At low and intermediate p_T, the results could be interpreted in terms of a later thermalization of charm quarks compared to light quarks, while at high p_T, path-length dependent effects seem to dominate. The J/ψ v₂ measurements are further compared to a microscopic transport model calculation. Using a simplified extension of the quark scaling approach involving both light and charm quark flow components, it is shown that the D-meson v_n measurements can be described based on those for charged pions and J/ψ flow. [Figure not available: see fulltext.]