Okay I know I stated this but now I'm definitely confirming that Aromatherapy activates Sap Sipper in double battles, if you have your partner use it alongside a Sap Sipper Pokemon. I don't think it works for the opposing side since the move only affects your own team, though. Still want to test Soundproof Vs. Heal Bell as Scorpdestroyer mentioned.
Also, the OP says that if one type is weak to Flying Press and the other resists, it hits for 1x damage...But from something that just happened to me today, I think it goes a step further: A Hawlucha used it on my Venomoth and it actually took NVE damage. So I'm guessing it counts the total amount of resistances in total? I know Bug + Poison both resist Fighting, cutting it to 0.25x, while Bug is weak to Flying and Poison is neutral, boosting it by 2x. And this is probably obvious af and I'm just rambling but I guess this means that it kind of uses some multiplicative formula looking at all the defender's resistances/immunities/weaknesses for both types (if applicable) to produce the effectiveness. So you could probably think like:
Fighting Vs. Type 1 * Fighting Vs. Type 2 * Flying * Type 1 + Flying * Type 2 = Effectiveness
Fi1 * Fi2 * Fl1 * Fl2 = E
So if you were attacking my Venomoth with it, it would be like:
Fighting Vs. Bug * Fighting Vs. Poison * Flying Vs. Bug * Flying Vs. Poison = Effectiveness, or in short:
0.5 * 0.5 * 2 * 1 = 0.5
SN: (Dear god, pardon the extremely sloppy attempt at making a math equation up there. This is what happens when you don't go to college, you force yourself to improvise)
And with an Immunity, you would automatically plug in a "0" to the equation, thus making it take no damage at all. Not totally sure if this means an 8x move is now openly possible, or even a 16x move by those standards. As far as I know, I don't think there's any Pokemon who has BOTH types 4x weak both to Fighting AND Flying, let alone the same for both types being 2x weak. So the highest you could possibly go is probably 4x, with one type being weak to Fighting and the other being weak to Flying with no resistances in between (Scrafty, for instance) since there's no overlapping weaknesses to both.