Affinity for artifacts and flashback

[John Cox]

Does affinity for artifacts count as an alternate casting cost? IE could I flashback a thoughtcast with snapcaster mage and pay less due to affinity?

[TVand]

Affinity is not an alternative casting cost; it is a cost reduction effect.

From rule 601.2e: "The total cost is the mana cost or alternative cost (as determined in rule 601.2b), plus all additional costs and cost increases, and minus all cost reductions."

Since flashback is an alternative cost, the answer to your question is yes.  You could flashback a Thoughtcast and you would still pay less.