  Elliptic flow, $v_2$, and triangular flow, $v_3$, are to a good approximation
linearly proportional to the corresponding spatial anisotropies of the initial
density profile, $\varepsilon_2$ and $\varepsilon_3$. Using event-by-event
hydrodynamic simulations, we point out when deviations from this linear scaling
are to be expected. When these deviations are negligible, relative $v_n$
fluctuations are equal to relative $\varepsilon_n$ fluctuations, and one can
directly probe models of initial conditions using ratios of cumulants, for
instance $v_n\{4\}/v_n\{2\}$. We argue that existing models of initial
conditions tend to overestimate flow fluctuations in central Pb+Pb collisions,
and to underestimate them in peripheral collisions. We make predictions for
$v_3\{6\}$ in noncentral Pb+Pb collisions, and for $v_3\{4\}$ and $v_3\{6\}$ in
high-multiplicity p+Pb collisions.
