[pushkins]

Before you lay the slate you will need to install a cement backer board to the existing floor.
After the existing floor is clean of all debris you trowel on a layer of thin set mortar then place the backer board on the mortar and screw the backer board down to the existing flooring material. There are 60 screws per sheet and a sheet covers 15 square feet. After the thin set has dried (24 hours) you can lay the slate tiles with thin set.
Never should any sort of tile be directly applied to wood sub floors.

If it were me I'd tile the entire room before the cabinets are set in place.
To save a little money you could always mark out where the cabinets will sit and tile just a little past this area, that way the cabinets will look like they sit on a full floor of slate.