  Flat-space holography requires a thorough understanding of BMS symmetry. We
introduce an oscillator construction of the highest-weight representation of
the $\mathfrak{bms}_3$ algebra and show that it is consistent with known
results concerning the $\mathfrak{bms}_3$ module. We take advantage of this
framework to prove that $\mathfrak{bms}_3$-blocks exponentiate in the
semi-classical limit, where one of the central charges is large. Within this
context, we compute perturbatively heavy, and heavy-light vacuum
$\mathfrak{bms}_3$-blocks.
