The story is set sometime shortly after the Stargate SG-1 series finale, "Unending." As such, it contains spoilers for that episode. If you haven't seen it -- and care about such things -- you probably don't want to read yet.
Oddly enough, Teal'c's voice was more of a challenge than Jack's -- for Jack, I just had to challenge my inner snarkiness. For Teal'c, though, I found it hard to mimic his stilted, overly-formal way of speaking without making it ridiculous.
One of the pairings is canon; the other is not, but hinted at.
My favorite section:
"But...Mitchell! He's -- he's a weenie."
Teal'c was fairly certain that Jack wasn't speaking of a hot dog -- which was his only reference for the word -- especially given the scornful tone to his voice, but he found nothing to say in response.