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Does Vulkan grant twin linking to units and models that don't have Combat Tactics, like Speeders with multimeltas or Dreads?

If you include Vilcan He'stan then all units in your army lose the Combat Tactics special rule. Instead, all thunder hammers in your army will count as master crafted, and all flamer, heavy flamers, melatguns and multimeltas count as twin-linked. If more than one yadda yadda.

Is it an exchange, like in Shrikes case, or a separate bonus applicable to all?

yes he does.

Yes, your Speeders and Dreads would get it. But I don't think a blanket statement "yes" is in order. If it Space Marine and comes from your Codex I would say yes.

The same shouldn't be true for Sister of Battle Allies as they do not meet the requirements for forgoing Combat Tactics.

I think it is just a poorly written rule that is going to cause troubles for time to come.

Although Kej is certainly entitled to his interpretation, RAW everything in the army gets the twin-linking. So your 2 SoB squads, your Celestian and her immolator, your Stormtroopers and their flamers, all benefit from He'stan's rule.

Any other reading is just wishful thinking, the codex is very explicit.

Ofc any DH/WH allies get it. Else any SM vehicles are going to be left without too.

And just stop to think of the army lists... Vulkan + compulsory troops is going to be a huge chunk of points off a normal SoB list. It might actually make them less competitive to sacrifice 30 footsloggers, 2 Rhino squads or two Exorcists for a few twin-linked weapons.

SoB can't take Vulkan as an ally choice. You have to run SM as the base list with SoB as Inquisitorial allies.