What kind of grout should be used for slate tiles installed on a patio
Presuming that you are laying on to a solid concrete base, you could use a polymer modified flexible grout or you could use a basic 4-1 Sand & Cement mix but use an additive with each mix to make it flexible & less susceptible to cracking. Another great product we have used is Geofix that is applied dry but sets very hard and is easy to apply.
You would need to seal the slate tiles prior to grouting so that the grout is easy to remove if you intend to slurry grout the joints.
The grout must be pushed down firmly and all joints well filled, as no air should be allowed to remain in the joints. The more grout used means it will set harder.