forbidden flame/flesh drop?

I've read that those jewels only drop on the uber version of eater and exarch, but earlier I did a run on 28th map run of exarch and dropped flame jewel, I don't have the thirst for knowledge node on atlas either, can that jewel drop from regular exarch run?

You don't need to run ubers to drop the normal Forbidden jewels. Ubers have their own variant that grant "hidden" ascendancy notables.

alright thank you.

It can even drop on the Quest version. Quest Exarch on league start dropped me one.