  We derive the first and second-order expressions for the shear, the bulk
viscosity, and the thermal conductivity of a relativistic hot boson gas in a
magnetic field using the relativistic kinetic theory within the Chapman-Enskog
method. The order-by-order off-equilibrium distribution function is obtained in
terms of the associate Laguerre polynomial with magnetic field-dependent
coefficients using the relativistic Boltzmann-Uehling-Uhlenbeck transport
equation. The order-by-order anisotropic transport coefficients are evaluated
in powers of the dimensionless ratio of kinetic energy to the fluid temperature
for finite magnetic fields. In a magnetic field, the shear viscosity (in all
order) splits into five different coefficients. Four of them show a magnetic
field dependence as seen in a previous study \cite{Ashutosh1} using the
relaxation time approximation for the collision kernel. On the other hand, bulk
viscosity, which splits into three components (in all order), is independent of
the magnetic field. The thermal conductivity shows a similar splitting but is
field-dependent. The difference in the first and second-order results are
prominent for the thermal conductivities than the shear viscosity; moreover,
the difference in the two results is most evident at low temperatures. The
first and second-order results seem to converge rapidly for high temperatures.
