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Do we think that Flamestorm Cannons benefit from Vulkan Hes'tan's "twin-liked" ability?
It doesn't. Only flamers, h.flamers, meltas, and multimeltas as they are the only things listed. So, technically, fusion guns aren't twin-linked either (if you had allied or something), even though they are basically just meltaguns.
If you want a quote:
"If you include 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 flamers, heavy flamer, meltaguns and multimeltas count as twin-linked."
-Codex: Space Marines, pg 93
Why his glove works is because it is "fired as a heavy flamer", so it falls into one of the above four weapon types. The flamestorm cannon, even though it's just a bigger flamer, isn't one of the four weapon types listed.