Is Coefficient of viscosity frame dependent? Why/Why not?
The viscosity could potentially be directionally dependent but in most common systems it can be assumed with good accuracy to be approximately isotropic.
A body in strength of materials is assumed to act like a spring while common fluids in fluid mechanics are characterised by energy dissipation. A fluid basically acts like a huge viscous dampener where the viscosity is the characteristic damping coefficient of the fluid. In theory this dissipation could be anisotropic (just like the stiffness tensor in strength of materials) but the commonly used formulation of the Navier-Stokes equations found in textbooks make use of isotropic Newtonian fluids. There are exotic substances such as para-azoxyanisol that have a flow-induced anisotropic viscosity (a different viscosity in flow direction, in the direction of the velocity gradient and perpendicular to the other two) or paramagnetic colloids under an external magnetic field. So in those applications your viscosity would change with orientation to the main flow or magnetic field. Furthermore eddy viscosity of turbulence models in rotating flows is highly anisotropic.