Both of these spells are different from what we are discussing.Dragon's Breath does create a new kind of action, as the spell description says. It is not an "attack" action, because it doesn't involve a roll to hit. That's why the spell description does not use the word attack.
Witch Bolt is different again. In the first round, the player takes the "Cast a Spell" action and as part of that gets to make a spell attack. Extra Attack does not come into play because they haven't made an Attack action. Subsequent rounds are not an attack, because there is no attack roll, and damage is done automatically.
Neither of these matches the case of Flame Blade. Casting it is a bonus action (not an action, involving "Cast a Spell"). When it comes time for the character to take an action, though, they make a "melee spell attack".
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