  We give a short proof that the ergodic sums 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.
