It's been awhile, but here are the basics to get you going.

Heat flux should be measured in Energy/Area and fairly easy to solve. Convert your Heater power output to an appropriate unit and divide by the surface area of your box. This of course assumes that the bax radiates energy evenly. And I would use the simplified outside area of the box, rather than including a complicating factor for the difference between the inside area and outside area.

The conductivity is a more interesting question. I don't remember the specific equations anymore. I could look them up for you, but it's your homework, not mine. It should be a function of temperature gradient, material thickness and your pre-determined heat flux. Wait. It should be in the form of Q=U*A*dT(log mean). Q being heat transfer, U is thermal conductivity of the system, A is area, dT(log mean) is the log mean temperature difference, though that should be the same as just dT in this case. That would give you the box thermal conductivity, but not the material conductivity. That will include a material thickness factor. You should of course verify all of this with an appropriate textbook.