if I install slate flooring or ceramic tile on advantech subfloor ,is it a good possibility the tile or slate will crack?

You can not tile on any subfloor, (unless it's concrete) you still need to put down an undderlayment. You should have at least an inch and an eighth of flooring under your tile or slate.If you install a 1/4" or1/2" concrete board over your advantech sub you'll be okay.Make sure you mortar the board down with a latex fortified mortar with a 1/4" notch trowel and seam the joints with mesh tape and mortar. You'll be good to go. Good luck.