  We present simultaneous radio through sub-mm observations of the black hole
X-ray binary (BHXB) V404 Cygni during the most active phase of its June 2015
outburst. Our $4$ hour long set of overlapping observations with the Very Large
Array, the Sub-millimeter Array, and the James Clerk Maxwell Telescope
(SCUBA-2), covers 8 different frequency bands (including the first detection of
a BHXB jet at $666 \,{\rm GHz}/450\mu m$), providing an unprecedented
multi-frequency view of the extraordinary flaring activity seen during this
period of the outburst. In particular, we detect multiple rapidly evolving
flares, which reach Jy-level fluxes across all of our frequency bands. With
this rich data set we performed detailed MCMC modeling of the repeated flaring
events. Our custom model adapts the van der Laan synchrotron bubble model to
include twin bi-polar ejections, propagating away from the black hole at bulk
relativistic velocities, along a jet axis that is inclined to the line of
sight. The emission predicted by our model accounts for projection effects,
relativistic beaming, and the geometric time delay between the approaching and
receding ejecta in each ejection event. We find that a total of 8 bi-polar,
discrete jet ejection events can reproduce the emission that we observe in all
of our frequency bands remarkably well. With our best fit model, we provide
detailed probes of jet speed, structure, energetics, and geometry. Our analysis
demonstrates the paramount importance of the mm/sub-mm bands, which offer a
unique, more detailed view of the jet than can be provided by radio frequencies
alone.
