Hmmm...I guess I wasn't clear earlier...6 mm (~1/4 ") old roof slate does not fare well on floors...
I am reluctant to even get into traditional lime tile bedding formulas and grouts, as I am worried of the strong potential for a great deal of work, money then having to tear it all up...
I do like Joe B's idea of "fragmenting it" into smaller pieces. I must strongly suggest...this needs to be done with a diamond wet saw. Just smashing with a hammer will only further delaminate, destabilize and degrade the slate.
If still wanting to move forward...the slate must be soaked in warm water, and bedded well in a mortar bed that is "just wet enough" not soupy...
I would recommend either of these companies for advice on which of their products to use and the proper mix...The are both great colleagues and probably the of the most knowledgeable in North America on lime, natural concretes, pozzolanics and related masonry products...Both great companies to work with...Feel free to name drop...
Natural Mortars Owner: Mike Edison
Lime Works Owner: Andrew deGruchy