Is/was there ever a 340 Magnum

IDK what you are asking.

Pic of the badge?

71/72 340 Dart and Demon (and 73 340 Dart Sport) could have 340 Magnum badges.

As could 71-73 340 Challengers.

71 340 Super Bee and 72/73 340 Rallye Chargers would have a larger badge.