welcome to GoY.

From what you have said I assume you don't intend to add plants to this area. I would put some fine material be it sand or fine gravel down to fill the gaps or the slate chippings will fall in the cracks.
you could also use garden membrane to stop the slate falling in the gaps but make sure it is a water permeable one or you will get standing water.

You don't have to use sand, but the substrate should be flat and level. Builder's sand is very pliable and makes the job, quick, easy and fun. This is exactly what it is for. It also won't crack as leveling concrete would do. I would definitely go with the leveling sand. After you apply it, spray it down with water to cause it to settle into the contours of the ground. Then apply another thin layer of sand on top to level the surface.

Fun???! Well, its whatever turns you on...Enjoy anyway!

LOL, It's easier then it may seem - once you have the right tools. The toughest part is clearing out all the old debris. With the sand, it's like frosting a cake on a larger scale. You can get creative with the slate chips, creating different patterns, using different colors, etc.