Does flanking a creature make it a surprise attack, meeting the requirement for the Assassin rogue's Assassinate feature?

Question

The optional rule on flanking (DMG, p. 251) says:

Flanking on Squares. When a creature and at least one of its allies are adjacent to an enemy and on opposite sides or corners of the enemy's space, they flank that enemy, and each of them has advantage on melee attack rolls against that enemy.

When in doubt about whether two creatures flank an enemy on a grid, trace an imaginary line between the centers of the creatures' spaces. If the line passes through opposite sides or corners of the enemy's space, the enemy is flanked.

Flanking on Hexes. When a creature and at least one of its allies are adjacent to an enemy and on opposite sides of the enemy's space, they flank that enemy, and each of them has advantage on attack rolls against that enemy. On hexes, count around the enemy from one creature to its ally. Against a Medium or smaller creature, the allies flank if there are 2 hexes between them. Against a Large creature, the allies flank if there are 4 hexes between them. Against a Huge creature, they must have 5 hexes between them. Against a Gargantuan creature, they must have at least 6 hexes between them.

The description of the Assassin rogue's Assassinate feature (PHB, p. 97) says:

Starting at 3rd level, you are at your deadliest when you get the drop on your enemies. You have advantage on attack rolls against any creature that hasn’t taken a turn in the combat yet. In addition, any hit you score against a creature that is surprised is a critical hit.

If I'm flanking a creature, is my attack considered a surprise attack?

Had a debate yesterday on whether or not Assassinate can be used every round or only in the first round of combat 'Surprise'. We decided or the latter. Is this correct?

Answer 1

Flanking makes no difference here, it is restricted to the 1st turn

Surprise only counts at the start of the combat in D&D 5e. As we can read in the PHB about The Order of Combat on page 189:

If you're surprised, you can't move or take an action on your first turn of the combat, and you can't take a reaction until that turn ends.

The first part of Assassinate works on a creature that has not taken a turn yet. Note the wording of surprise, above: the creature still has a turn, it just cannot do anything. Thus it is limited to the first round (and also by initiative).

The second part of the feature requires the target to be surprised to grant the automatic crit, and thus will also only work in the first round.

Neither of these triggers are tied to flanking or having Advantage from other sources, all the information about them is contained in their description.

Note: It is possible you confused Assassinate for Sneak Attack here, as that can be used every turn, if you have Advantage (eg. due to flanking) or satisfy other conditions. These two are completely separate features, and do not "fuse together" or depend on each other (like what we see with barbarian Rage and other class features). The triggers are evaluated separately, and you can trigger neither, one or both of them in different situations.