Fic writers vary quite a lot in their portrayal of Kris' speaking: some have them completely or largely mute, whilst others have them talkative like any other character. What influenced your view on how much they speak and what speech mannerisms they have?
Coming out swinging with a tricky question right out of the gate, I see! I'm a little hesitant to answer this, but you've asked so I'll do my best!
The interesting thing about Kris as a character is that, while we know they are capable of speech, we only ever hear it second-hand from other characters. That, combined with the game trying to make them into a self-insert (which for the record they are not) can make the way they talk very much up to interpretation. To that end I don't necessarily think there are "right" or "wrong" ways to characterise their speech - or indeed their lack of it.
All of which is a prelude to me saying - it largely depends on what would work best for the story I'm writing. For longer fics where Kris takes centre-stage, such as A Heart, Frozen in Time or Through Shattered Glass, it makes sense for Kris to talk more and be more expressive through their vocalisations - though I do try and give them a more disaffected, clipped sense to their speech. Not quite robotic or perfunctory, exactly, but more that they choose their words carefully for maximum impact. Of course, during more emotional moments, I expect they'd have trouble keeping their utterances under such rigorous control, which I feel provides an interesting contrast!
(It must be remembered that Kris is a teenager in an American-style setting, and I take that into consideration whenever the situation may call for them to act more... like a teenager.)
Of course, other fics have them be completely mute, or selectively mute. The two fics that come to mind here are Where Our Shadows Cross and A Heart, Brimming With Light, where Kris doesn't utter a single line of dialogue. But again, the reasons for doing so here are different. In the former, I wanted Kris to be mute as a reflection of their unique character and their struggles to articulate themself, in contrast to Susie and Ralsei's struggles. In the latter, though, Kris not speaking is more a literary device to draw a sharper contrast between them and RepliKris - the Kris-golem-darkner that Ralsei winds up creating in the first chapter after his friends leave him all alone in the dark. Compared to the relatively inexpressive Kris, RepliKris is almost verbose, constantly professing their admiration for Ralsei or snarking against their foes - which highlights the wish-fulfillment nature of the character, and the way that that "ideal" version of Kris isn't necessarily true to life.
...I don't know if that has answered your question or not, Bleak. You're free to ask for clarifications if I was unclear at any point, or if you meant something else! But either way, I hope this has proven enlightening in some capacity!