"I will be starting with kailitypes then to PD.
Do I need seperate trays for each process?"

I don't believe separate trays are absolutely necessary for kallitype and palladium. Or separate brushes for that matter. Except for the fixing step needed in kallitype the two processes are virtually identical in the way we make the print. Same developers, same clearing baths, etc. I use the single tray method for processing all large kallitypes and palladiums and have never seen any sign of contamination. Probably the most important thing is to make sure you clean the coating brush well between the two processs, but even in this area nothing dramatic will happen if you do not because a little silver salt additive is not incompatible with making a palladium, and a littlle palladium salt additive is not incompatible witth making kallitypes.