Flame Blade is a 2nd level spell, and a very weak one:
You can use your action to make a melee spell attack with the fiery blade. On a hit, the target takes 3d6 fire damage.
This is on average 10.5 damage, while Shillelagh does 7.5 with 16 Wis, with 20 Wis it is 9.5.
So in exchange of 1 damage, Shillelagh does not need Concentration, and its damage type is also more beneficial. A lot more creatures resist Fire than are vulnerable to it, but magical bludgeoning can affect everyone.
Comparison to Flaming Sphere
Flaming Sphere does the same type of damage and also needs Concentration, but it is usable with a bonus action, has the chance of damaging multiple enemies, and does half damage even if the enemy saves successfully. If we assume (as the DMG does) that attacks can easily be converted to saves, and take a 50% hit chance, both spells have the same damage output.
While sustaining Flaming Sphere, you can use a cantrip with your action, giving further advantage to it.
So for the same investment (same spell slot, concentration, all your available actions) you can do much higher damage with the combination of a cantrip + Flaming Sphere.
While concentrating on one of these spells, you see Treant approaching. You cast Blight with your action. If you used Flaming Sphere you did 8d8+2d6 damage this turn, but only 8d8 with Flame Blade.
The initial damage is 4d6 and it increases with 1d6 per spell level, instead of every second one. This is still weaker than Shillelagh + Flaming Sphere, but at least now it has some use cases.
FB2: Flame Blade with 2nd level slot
FBm: Flame Blade with the highest available spell slot
Sh + FSm: Shillelagh as the action, and Flaming Spehere with the highest available spell slot as the bonus action
So the questions:
1) Did I miss something, can this get overpowered in some situations?
2) Would another 1d6 be overpowered? It is still less than Flaming Sphere + Produce Flame after level 11