What packing material to use between a brick and house beam?
Use stacked steel plates as shims. Use varying thickness's as required to ensure they are tightly packed and fully supporting the joist loads.

I'll assume the remaining structure of bricks and whatever is supporting them is properly designed and constructed, not just dry stacked (unless this is temporary, in which case do what ever works). If you live in a seismic area, the top of the bricks need to have a positive connection to the joists, not just shimmed. Your proposal sounds a bit sketchy on the surface, but it is possible to do this well and correctly, so I'll give you the benefit of any doubt and just answer your question.