What is the ninja's most up to date rotation?

[UBERHAXED]

(jug here if you're not stunning in the fight and boss is fully immune)

Might be worth nothing that you can change effect to silence...

The above is "okay" for an opener (see below, but warning, it contains cooldowns, which you didn't want). For the OP, outside of opener, prioritize in this order:
[Below 1 means Spinning Edge and 2 means Gust Slash]
1. Keep Huton up
That means 1-2-Armor Crush, if you don't have Huton for some reason, then you need to manually cast it with Ninjustu.

2. Keep Ninjustu on Cooldown
As a corollary, keep Trick Attack on cooldown. This means in single target you should use Suiton (+Trick Attack) followed by 2 Raiton. Since you should also be keeping all cooldowns off cooldown (i.e. use all cooldowns when available), including Kassatsu, you 7 every 2 minutes. You also shouldn't use Kassastu when your Ninjustu is not on cooldown. If you lost Huton, then you need to prioritize this first. If you fell out of the loop as a result, prioritize keeping Trick Attack on cooldown.

3. Keep Slashing Debuff up
Meaning 1-2-Dancing Edge
It should be clear here that slashing debuff (and your damage stances for that matter) does not affect Ninjustu aside from Fuma Shuriken and it (Slashing Debuff) doesn't affect DoT damage aside from the initial hit. Other than that, it's sort of like always having Blood for Blood (on that target) up. That said, Blood for Blood affects everything and your damage stances to affect the damage of DoT ticks.

4. Keep DoTs up
If you have to choose, go for Shadow Fang first (1-Shadow Fang) then Mutilate.

5. Use Aeolian Edge
That means 1-2-Aeolian Edge. It's your highest potency non-Dot, on GCD move. So you should be using it when you have nothing else to do.

Luckily, after the opener, this follows nicely into a (GCD) rotation because the timing lines up:
Opener-> 1-> 2-> Armor Crush-> 1-> Shadow Fang-> 1-> 2-> Dancing Edge-> 1-> 2-> Armor Crush or Aeolian Edge-> Mulitate-> 1-> Shadow Fang-> 1-> 2-> Dancing Edge-> (repeats from here) 1-> 2-> Armor Crush
Because buff timers will be attack different places depending on GCD, just keep in mind that it's better that DoT don't clip if you can avoid it, and it better for Slashing debuff to clip if the alternative is to let it fall off.

As for the opener, assuming you don't use consumables:
Pre-pull 21.5 seconds -> Huton
Pre-pull 1.5 seconds (20 seconds later) -> Suiton (Hold for pull obviously)

Pull -> (Off GCD moves in parenthesis)
(Cast Sution, i.e press the Ninjustu button)-> 1-> (Kassatsu + Internal Release) -> 2-> (Blood for Blood) -> Dancing Edge -> (Jugilate) -> 1 -> (Trick Attack) -> Shadow Fang -> (Raiton) -> Mutilate -> (Mug) -> 1 -> (Dream within a Dream) -> 2 -> (Duality) -> Aeolian Edge -> 1 -> 2 -> Dancing Edge -> Rotation

If you use a potion, then you can replace the Jugitate after Dancing edge with it and use Jugilate after Aeolian Edge. The whole theory behind the opener (as every opener) is to maximize damage by doing the highest potency moves under the largest amount of buffs.