With 1.06×108 ψ(3686) events collected with the BESIII detector, the branching fraction of ψ(3686)→ωK+K- is measured to be (1.54±0.04±0.11)×10-4. This is the most precise result to date, due to the largest ψ(3686) sample, improved signal reconstruction efficiency, good simulation of the detector performance, and a more accurate knowledge of the continuum contribution. Using the branching fraction of J/ψ→ωK+K-, the ratio B(ψ(3868)→K+K-)/B(J/ψ→K+K-) is determined to be (18.4±3.7)%. This constitutes a significantly improved test of the 12% rule, with the uncertainty now dominated by the J/ψ branching fraction.