Hidden appearances, worth farming multiple difficulties?

Trying to go for Taeshalach

Just wondering if it’s worth going through LFR, Normal, Heroic, and Mythic every week or is it just 1 chance per week?

From what I understand, it’s just once per week on a character. But you can run multiple characters. I got mine doing LFR version.

I got mine doing LFR as well. Its much faster and i believe the chance is the same, regardless of difficulty. The only appearance you need to be on Mythic for is the red Scythe of The Unmaker.

Do you know if the flame sword will drop with a bm hunter or if I need to be surv spec for it to work?

It will drop for any spec, but the class needs to be one that can use a 2h sword. Spec doesn’t matter, but I was a Survival Hunter anyway so it didn’t make a difference. If you’re really worried, you can change your loot specialization to Survival even if you aren’t current using the spec.