If you are revered with Valarjar, you should get the [Boon of the Salvager] enchant from Valdemar Stormseeker at Stormheim. It allows you to sometimes loot [Salvaged Armor] which can contain extra Felslate or Leystone Ore.

Felslate


Legion introduces three new items that you can use to speed up farming ores. These three items are: [Leystone Hoofplates],[Demonsteel Stirrups], [Stonehide Leather Barding]. You should use these if you can find them cheap on the Auction House, or craft it yourself if you can. Every mobs scales to your level in Legion, so it will be a lot harder to avoid the mobs attacking you while you try to farm ores. The combination of these three will make farming ores a lot easier, but the one I would recommend the most is [Demonsteel Stirrups], which let's you mine ores while mounted.
You should also enchant your gloves with [Legion Mining].
SuramarThis is best place to farm Felslate, and actually the only place where you can reliable get Felslate from creatures. It's seems there is always a few Felfire Basilisk up at the marked area, so you should have no downtime.
Since this is the only place for farm Felslate, probably a lot of other players will farm here too, and this is also a quest area, so it can get a bit annoying sometimes when a lot of players are here tagging your mobs but they don't loot the corpses and you can't mine them.
If there are too many players here, you should just leave and use the farming routes below.

Val'SharahFelslate is a rare spawn of Leystone, so you will mainly find Leystone.

SuramarSame as above, you will mainly find Leystone.
Suramar is a level 110 zone, so you can't farm here at lower levels.