  We give a short proof that the ergodic averages of $\mathcal{C}^1$
observables for a $\mathcal{C}^1$ flow on $\mathbb{T}^2$ admitting a closed
transversal curve whose Poincar\'e map has constant type rotation number have
growth deviating at most logarithmically from a linear one. For this, we relate
the latter integral to the Birkhoff sum of a well-chosen observable on the
circle and use the Denjoy-Koksma inequality. We also give an example of a
nonminimal flow satisfying the above assumptions.
