  With $1.06\times 10^8$ $\psi(3686)$ events collected with the BESIII
detector, the branching fraction of $\psi(3686) \to \omega K^+ K^-$ is measured
to be $(1.54 \pm 0.04 \pm 0.11) \times 10^{-4}$. This is the most precise
result to date, due to the largest $\psi(3686)$ 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 $J/\psi \to \omega K^+ K^-$, the ratio $\mathcal{B}(\psi(3868) \to
K^+K^-) / \mathcal{B}(J/\psi \to K^+K^-)$ is determined to be $(18.4 \pm
3.7)\,\%$. This constitutes a significantly improved test of the $12\,\%$ rule,
with the uncertainty now dominated by the $J/\psi$ branching fraction.
