  We consider decays of $B$ and $K$ mesons into a pseudo-scalar or vector meson
plus missing energy. Within the SM, these modes originate from flavor changing
neutral current (FCNC) processes with two neutrinos in the final state. In this
paper we consider the experimental upper bounds on these modes and interpret
the difference between these bounds and the SM prediction as a window into new
light invisible particles. In particular we consider the case where some new
symmetry requires the new particles to be produced in pairs. We first construct
the general low energy effective Lagrangian coupling an FCNC with two dark
sector particles of spin zero, one-half and one. We then present numerical
estimates for the constraints that can be placed on these interactions, finding
that an effective new physics scale from ${\cal O}(10)$-${\cal O}(10^{11})$ GeV
can be probed, with the exact value strongly depending on the interaction
structure as well as the mass of the invisible particle. For $K^+\to \pi^+
\displaystyle{\not} E$ we incorporate into our constraints the effect of using
only the signal regions of NA62, and for $B^+\to K^+ \displaystyle{\not} E$ the
$q^2$-dependent efficiency of Belle II.
