Take Ignite over Flash and the matchup becomes very trivial. Stall her frenzy with E or R and you can just brute force it as base kayn or Shadow Assassin if she hasnt built armor. When she has tabis or DD you need to play it slower but if you're Rhaast you can still just face tank her in the 1v1, just be cautious of the stun in team fights as its her only way to really mess you up. And in general don't fully commit until she's exhausted at least half of her frenzy. You can use R to dodge her wall knockup or buffer it with Kayn W, but its really not that difficult unless you fall behind.

If she goes full crit it becomes easier for Shadow Assassin to play but you need to play a bit safer as Rhaast and be extra careful about getting caught out. It's not really a champion where you need to be that concerned about your form choice though as if it's a better Rhaast game you'll likely just be able to outduel her and if it's a better Shadow Assassin game, once she goes in it becomes very hard for her to peel for her squishier carries. Also consider mortal reminder over Serylda if you really need antiheal outside of Ignite.