Chance Encounter/As Luck Would Have It and reflips/rerolls
As Luck Would Have It works fully with rerolls.
Chance Encounter doesn't work with reflips.
The entire game only sees one result from any kind of Krarkish prestidigitation.


Mark Rosewater (the Un-Rules Manager) rules on Goblin Bookie/ALWHI in this blog post:

mikedoesstories asked: If I use Goblin Bookie to reroll a die, do both die rolls count for As Luck Would Have It or just the rerolled die?
Both rolls count.

MaRo later clarifies that it's based on whether the dice roll would trigger this ability regardless of the outcome (posted here):

tarectarec asked: In your FAQ you said that As Luck Would Have It would get counters from the original dice in case of a reroll. But would Chittering Doom give me a squirrel token if I rolled a 6 but then decided to reroll it (Rolling a 1 this time for example)?
No. Counting die rolls is different than triggering things based upon on a particular outcome.

This wouldn't work with Krark&#39;s Other Thumb since you're specifically instructed to ignore one of the rolls (as far as the rest of the game is concerned, it never happened). For the same reason, Krark&#39;s Thumb won't work with Chance Encounter.

By following this logic in the second case, we can see that a reroll can't trigger Chance Encounter twice because Chance Encounter only triggers on a particular outcome (rather than the flip itself), and there's only one outcome.
Note that we're safe following un-logic in this case, as reflips and rerolls can currently only exist in silver-border.