As long as the slate has not been exposed to anything bad it is fine to use in aquariums. However, if it is in public land, the local council might have sprayed it with herbicide. If it is in your backyard and you don't use chemicals (pesticides/ herbicides) it should be safe.
Give it a good rinse under the tap and soak it in a bucket of fresh water for a week. Take it out and rinse it off each day, and replace the water in the bucket. After a week it should be safe to go in your tank.