Jacketch says:
Would doing an arcana check count as an action, or can I just do it with Kit's advantage? I'm gonna post as of the answer was yes, I'll delete it if it's no.
It would take an action, yes. This falls under "Improvising an action" on p. 193 of the Player's Handbook where it gives many examples of using an action to do skill checks: breaking down doors (athletics), intimidating enemies (intimidation),sense a weakness in a magical defense (arcana), or calling for parley with a foe (persuasion). If skill checks were free actions, players would just spam intimidation checks every round, and so would every monster!
McDunno says:
Kit's not proficient in Arcana, so he's taking the Help Action to give Pageflap advantage on an Arcana check to see if he can figure out what this thing's doing and how it can be defeated. If this doesn't use up an Action, Kit will re-cast Dancing Lights.
"That squiddy thing seems to pulse brighter when magic is used! What do you make of it?" makes for great dialogue but does not warrant the Help action. You're just pointing out the obvious and asking for his opinion. If you walk into the doctor's office and say "Hey Doc, look at this bump on my head, what do you think?" It doesn't make the doctor any better at diagnosing what's wrong with the bump, it just gets him started on his investigation.
I think Kit should leave it as flavourful dialogue, and Pageflap just does a regular arcana check. As you suggested, use Kit's action to cast Dancing Lights or something else - your call :)