Chinchilla and chin chiller are not pronounced quite the same**, at least not necessarily. So at one extreme, we would have a case of mispronunciation; at the other, a case of mishearing.
As for how it should be written, I favour:
Character B: "I just bought a chinchilla."
Character A: "What's a chin chiller?"
Character B: "Chinchilla."
if only because it captures what's probably been said. If the written text has character A saying "chin chiller," I, as a reader, would believe him to be trying to confuse character B.
Here's an example of something similar from near the end of my WiP1:
“I have received your email. The attachments contained a virus called Lodz. My system has refused them.”
“Really, sir? There can’t be. There isn’t a Lots virus. Oh, you mean Łódź.”
“Ooodzh?”
“Almost. Łódź.”
The warning in the email has that word spelt as Łódź, but the first speaker (a German speaking in English) ignored the Polish accents, and said, "Lodz". Note that z is, in German, pronounced as "ts", which is why the second speaker (an Italian speaking in English) repeated the word as he heard it, i.e. "Lots***." He then said the word how he would, which the first speaker heard as "Ooodzh" (where the zh is pronounced the same as the s in treasure or leisure). That isn't quite right, at least in the opinion of the Italian****, so he merely repeated, "Łódź."
** - Just try saying them both out loud. When I do so, the second syllable of chinchilla is slightly shortened and there's not much emphasis on the first syllable, chin. With chin chiller, both chin and chill are emphasised approximately equally and they're of about the same duration.
*** - I'm winging this a bit. I believe that a d at the end of a word is pronounced "t", so lodz could be "lotts", in the same way as Todt is "Tot". (I'm not sure, but I think the extra consonant is there to change the length of the preceding vowel, shortening it. Which is why the vowels in Berlin - Bearleen - are long: each syllable ends with a single consonant. Possibly.
)
*** - I wouldn't have dared have used a Polish character in this scene, as I've only ever heard the word, Łódź, said by an English football commentator during a Euro 2012 match at Łódź. (By the way, this exchange has been in my WiP1 for six or seven years.)