  Let $(X, \phi)$ be a compact metric flow without fixed points. We will be
concerned with the entropy of flows which takes into consideration all possible
reparametrizations of the flows. In this paper, by establishing the
Brin-Katok's entropy formula for flows without fixed points in non-ergodic
case, we prove the following result: for an ergodic $\phi$-invariant measure
$\mu$,
  $$ h_{top}^{B}(\phi, G_{\mu}(\phi))=h_{\mu}(\phi_{1}),$$
  where $G_{\mu}(\phi)$ is the set of generic points for $\mu$ and
$h_{top}^{B}(\phi, G_{\mu}(\phi))$ is the Bowen entropy on $G_{\mu}(\phi)$.
This extends the classical result of Bowen in 1973 to fixed-point free flows.
Moreover, we show that the Bowen entropy can be determined via the local
entropies of measures.
