  We develop the framework that reveals the intrinsic conserved stress tensor
and current associated with the null infinity of a three-dimensional ($3d$)
asymptotically flat spacetime. These are, respectively, canonical conjugates of
degenerate metric and Ehresmann connection of the boundary Carrollian geometry.
Their conservation reproduces the Bondi-mass and angular momentum conservation
equations if the asymptotic boundary is endowed with a torsional affine
connection that we specify. Our analysis and results shed further light on the
$3d$ flat holography; the stress tensor and current give rise to an
asymptotically flat fluid/gravity correspondence. The requirement of a
well-defined $3d$ action principle yields Schwarzian action at null infinity
governing the dynamics induced by reparametrizations over the celestial circle,
in accord with the codimension $2$ holography of $3d$ flat spacetimes.
