  The discovery of rapid synchrotron gamma-ray flares above 100 MeV from the
Crab Nebula has attracted new interest in alternative particle acceleration
mechanisms in pulsar wind nebulae. Diffuse shock-acceleration fails to explain
the flares because particle acceleration and emission occur during a single or
even sub-Larmor timescale. In this regime, the synchrotron energy losses induce
a drag force on the particle motion that balances the electric acceleration and
prevents the emission of synchrotron radiation above 160 MeV. Previous
analytical studies and 2D particle-in-cell (PIC) simulations indicate that
relativistic reconnection is a viable mechanism to circumvent the above
difficulties. The reconnection electric field localized at X-points linearly
accelerates particles with little radiative energy losses. In this paper, we
check whether this mechanism survives in 3D, using a set of large PIC
simulations with radiation reaction force and with a guide field. In agreement
with earlier works, we find that the relativistic drift kink instability
deforms and then disrupts the layer, resulting in significant plasma heating
but few non-thermal particles. A moderate guide field stabilizes the layer and
enables particle acceleration. We report that 3D magnetic reconnection can
accelerate particles above the standard radiation reaction limit, although the
effect is less pronounced than in 2D with no guide field. We confirm that the
highest energy particles form compact bunches within magnetic flux ropes, and a
beam tightly confined within the reconnection layer, which could result in the
observed Crab flares when, by chance, the beam crosses our line of sight.
