Does Not so Fast counter King's Edict?

No, Not So Fast cannot counter King's Edict.

According to the card text and official rulings, Not So Fast can only counter a spell or ability that "chooses" a friendly unit or gear. King's Edict does not target or choose units when it is played; instead, it instructs each opponent to make a choice during the resolution of the spell.

As established in RiftJudge FAQ #509 and FAQ #8616, choices made by players as instructed by a spell's resolution are distinct from the spell itself "choosing" or "targeting" a unit. Because King's Edict does not contain the word "target" or "choose" as part of its initial play requirements, it does not meet the criteria for being countered by Not So Fast.