What is the best/fastest way to Farm railjack intrinsics.

Intrinsics gain is based on Affinity so the old method of going into a high level Skirmish and using Ivara/Equinox/another sleep ability to get Stealth melee kills works still.

Getting Intrinsics is pretty easy to just do passively now as well though, I'd personally just go through doing other Railjack farms (like Sevagoth) and you'll get them pretty quickly over time.

The Banshee affinity farming method should work as long as you have all of the requirements to do it.
Banshee + Savage Silence augment + 200% Ability Strength and 150-200% Duration, 100% range.
Equip Prime Sure Footed, or Power Drift + Fortitude + Sure Footed to become stagger immune.Subsume Gloom over her 1 or 4.
Equip Kuva Bramma, or an equivalent giant aoe-nuke weapon that can clear a room with only one shot.

When the mission starts (Exterminate mission is probably best), turn on gloom and her 3 (Silence).
Her Silence+Augment ability will stun enemies when you get near-ish. And the Gloom will extend that stun duration from 1s to like 5-8s.
The enemies cannot detect you or become alerted during this time. So you can run through the mission with your Bramma or other nuke and just blow up everything while maintaining your stealth affinity multiplier because nothing is ever detecting you other than Eximus units. Bring a sentinel with no gun on it. Carrier Prime for Bramma ammo is probably best. Try to use Enemy Radar Aura + Enemy Radar on Sentinel so you know where to aim your nukes to clear the room quickly before the enemys become alerted.

This is basically the best way to farm affinity in the game, though it does have a lot of different requirements. You can also use it to farm Focus from Telesto, Saturn with Focus Lens and usually hit focus cap within a few mission runs.

I am not 100% sure, but since Railjack Intrinsics are based on Affinity, having a 2x Affinity booster should also technically be equal to 2x intrinsics gained.

If you do not meet these requirements or do not have the ability to meet these requirements, then just equip Ivara and go to a Spy or Exterminate mission and just sneak around and sneak-finish all the enemies with melee. Its not as fast as using the Banshee method but it is still decent.

Stealth kill all the enemies on the crew ships and stations. Build that stealth multiplier. Kill the big guys only after you have the 500% multipler. Use the naramon school for the +45% affinity from melee kills.

I got the most with stealth kills running through Corpus Spy missions. I imagine endurance runs might have higher gain though.