The second (v 2) and third (v 3) flow harmonic coefficients of J/ψ mesons are measured at forward rapidity (2.5 < y < 4.0) in Pb-Pb collisions at √ s NN = 5.02 TeV with the ALICE detector at the LHC. Results are obtained with the scalar product method and reported as a function of transverse momentum, p T , for various collision centralities. A positive value of J/ψ v 3 is observed with 3.7σ significance. The measurements, compared to those of prompt D 0 mesons and charged particles at mid-rapidity, indicate an ordering with v n (J/ψ) < v n (D 0) < v n (h ±) (n = 2, 3) at low and intermediate p T up to 6 GeV/c and a convergence with v 2 (J/ψ) ≈ v 2 (D 0) ≈ v 2 (h ±) at high p T above 6-8 GeV/c. In semicentral collisions (5-40% and 10-50% centrality intervals) at intermediate p T between 2 and 6 GeV/c, the ratio v 3 /v 2 of J/ψ mesons is found to be significantly lower (4.6σ) with respect to that of charged particles. In addition, the comparison to the prompt D 0-meson ratio in the same p T interval suggests an ordering similar to that of the v 2 and v 3 coefficients. The J/ψ v 2 coefficient is further studied using the Event Shape Engineering technique. The obtained results are found to be compatible with the expected variations of the eccentricity of the initial-state geometry.