I know you have been around for a while but, have you read this yet? READ THIS FIRST
I second what pnut & Chris have posted. Your side blast wash tub forge will probably be ok for a while but for the kiln you will want to line it with Kaowool ridigized (at least 2 inches) and use a refractory like Satanite or Kast-O-Lite 30 (available from this forum). The kiln needs insulation.
https://www.iforgeiron.com/forum/257-insulation-and-refractories/
If you haven't yet mixed up the fire clay mix, just eliminate the cement and it will be adobe which will work better. If you have already used the cement mix just replace it with adobe when it falls apart. I noticed that the picture you posted is from Tim's post about building the forge.