By strictest reading, the weapon crits but the spell does not.
Firstly, extra damage dice are never multiplied on a crit. Flaming weapons are essentially a spell in the weapon, and they're not multiplied either.
Secondly, the spell requires no attack roll. It automatically hits if the weapon it's stored in hits, and thus is not subject to being a crit through the spell rules as well.
Now, if you were to make the spell within the weapon require an attack roll of it's own when the weapon hits, it would solve both issues (since it's now a spell that requires an attack roll and the damage dice of the spell are the base damage, not extra) and would allow the channeled spell to crit.