My Koffing used its "Smokescreen" attack on the Defending Pokemon which was already Confused. If that Pokemon attacks during my opponent's next turn, do they flip 2 coins and the attack fails if both coins aren't heads?
No, your opponent must flip each coin separately. First, flip a coin for the effect of Confusion. If the first flip is heads, then flip a second time for the effect of Smokescreen.
Source: HeartGold & SoulSilver FAQ (2010-02-11), PUI Rules Team (2010-02-11), PUI Rules Team (2014-09-25), TPCi Rules Team (2016-01-07)

Relevant cards

Note: All applicable cards may not be listed below.
COL1_60
HGSS1_70
PL3_65