Maybe I can settle the debate. I'll start by stating for the record that I am not a mechanic, nor am I an installer. I did work on tables for a few years in the early 90s, but my experience in the field pales in comparison to either of you.
My family has a long history of working with rocks and minerals. My great grandmother and her second husband worked the silver mines at Calico in California. She discovered and named more than one variety of stone found in the area. My grandfather was a gemologist. My uncle was one of Morrison Knudsen's top geologists--and to this day holds several world records for tunneling speed.
While I do not hold a degree in geology, I've had more than enough education (both formal and informal) to hold one. I am also an amateur jeweler and stone carver. I cut and polish each and every stone I use in my work. It's safe to say I know quite a bit about stone.
Actually, the mere mentioning of the surface 'flaking' is generally considered proof that it is slate. Slate fractures in thin layers, like shale. Brunstone fractures in chunks, like a chocolate bar.
Brunstone is a sandstone. Sandstone forms in much the same way as shale. The main difference is in the size of the particles. Each year there is seasonal runoff which carries with it bits of eroded stone. When the running water of a river slows down, the particles of eroded rock fall out of suspension. The largest particles fall out first, and the finest particles fall out last. Sandstone and shale are sedimentary rocks, while slate is a metamorphic rock. Sandstone, as the name implies, is composed of sand deposits that have been compressed over time. Shale is composed of compressed silt deposits. Shale and sandstone both form in layers. Given enough time and pressure, shale will turn into slate. Sandstone, on the other hand, turns into quartzite, which is not really important here.
As more and more material is deposited on top of shale, it begins to compress and heat up. As the heat and pressure build, chemical bonds break, and many new ones form. The new minerals form in flat plates perpendicular to the direction of force. This is what gives slate such great cleavage. Because sandstone forms in layers, it can often have a similar cleavage to slate. Just because a stone can be chipped into nice flat flakes is not enough evidence to call that stone slate.
An important distinction between slate and sandstone lies in the way it is quarried. Slate's cleavage is so good that it is split into pieces slightly larger than needed on site. First, a diamond saw is used to cut down into the slate, across it's layers, around five inches deep. Then a forklift comes along and literally scoops up the pieces by splitting it from the edge and then sliding the forks under the slab. Sandstone is quarried into large blocks, which are then cut into slabs on a saw.
If there's any ridges running across the surface in dark straight lines anywhere from 2" to 4" wide, that's cause by the sticker boards that was use to separate the pieces during their drying stages, which prevented the covered area by the sticker boards from fully drying resulting in a ridge you can feel.
Not all dark lines are caused by boards. Sometimes, they are actually a part of the stone as it existed in nature. If you'll notice in the picture below, the dark line (outlined in red) actually wraps around the end of the of the stone. This wouldn't happen from boards placed between slate sets. This discolored area is actually a distinct layer of stone. It ran nearly perpendicular to the finished playing surface.
Because slate is mined the way it is, the layers always run parallel to the playing surface. You might see a darker or lighter layer in a piece of slate, but it will never cross from top to bottom. This only becomes possible when a stone is quarried on large blocks and sawn into slabs. Conclusion, this is not slate.
https://imgur.com/a/zYylv