  We present first results from a series of $NuSTAR$ observations of the black
hole X-ray binary V404 Cyg obtained during its summer 2015 outburst, primarily
focusing on observations during the height of this outburst activity. The
$NuSTAR$ data show extreme variability in both the flux and spectral properties
of the source. This is partly driven by strong and variable line-of-sight
absorption, similar to previous outbursts. The latter stages of this
observation are dominated by strong flares, reaching luminosities close to
Eddington. During these flares, the central source appears to be relatively
unobscured and the data show clear evidence for a strong contribution from
relativistic reflection, providing a means to probe the geometry of the
innermost accretion flow. Based on the flare properties, analogy with other
Galactic black hole binaries, and also the simultaneous onset of radio
activity, we argue that this intense X-ray flaring is related to transient jet
activity during which the ejected plasma is the primary source of illumination
for the accretion disk. If this is the case, then our reflection modelling
implies that these jets are launched in close proximity to the black hole (as
close as a few gravitational radii), consistent with expectations for jet
launching models that tap either the spin of the central black hole, or the
very innermost accretion disk. Our analysis also allows us to place the first
constraints on the black hole spin for this source, which we find to be $a^* >
0.92$ (99% statistical uncertainty, based on an idealized lamppost geometry).
