That appears to be sandstone, and I have heard mixed results on using it in aquariums, as it can contain a lot of different metals and minerals. If you want to try it, you should consider that vinegar test. You also want to then consider leaving it in a bucket of water for a couple weeks, and testing that water to see if it changes its chemistry.
Where did you get the rock from? If you bought it at a fish store, then I would hope it would be safe to use.
Interested to hear what other people have to say about it.