No, War Magic doesn't allow multiple bonus-action attacks.
War Magic gives you one weapon attack as a bonus action.
Extra Attack can be used when you use the Attack action.
The two are completely and deliberately different; "an attack" is not the same as "the Attack action".
The knight gains the ability to make an extra attack, not the echoes.
The echo knight is who is granted the extra attack by Unleash Incarnation and the feature says this extra attack is granted, if the knight decides to use the feature, when she takes the Attack action.
The feature also allows for the knight to choose to make that additional attack (and not the knight's normal attacks) from the echo's location.
The important point here is that the echo itself is never granted an attack.
When the Unleash Incarnation feature is later improved by the Legion of One feature, the echo knight still only has the one extra attack but, owing to the fact that Legion of One allows the knight to have two echoes simultaneously, the knight can choose which echo's position to make that attack from.
The knight can make additional extra attacks from Unleash Incarnation only if it can take the Attack action additional times. The obvious way of doing this is through the fighter's Action Surge ability. Crucially, the same limitation applies: each additional time the Attack action is taken, only one extra attack is granted.
Quick side note: Haste would not grant the opportunity to use Unleash Incarnation because the spell explicitly limits the attack action it can grant to a single attack. See Does the Echo Knight fighter's Unleash Incarnation feature add another attack to the additional Attack action from the Haste spell? for more info.
To spell it out more directly, a fighter of 18th level would typically have 3 attacks per Attack action. Using Unleash Incarnation with the Attack action would give the fighter a 4th attack. If the knight Action Surges, it could do that again for 8 total attacks, excluding any potential attack granted by its bonus action.
Note that if the knight did have an attack available through a bonus action (such as from the Great Weapon Master or Polearm Master feats), this would not allow the knight to use Unleash Incarnation yet again, because that bonus attack is not granted by "taking the Attack action", which is the necessary prerequisite for getting Unleash Incarnation's extra attack.
Best Answer
Unleash Incarnation cannot exceed haste's limit
Haste states that the target
Haste does not set a baseline of one attack to which you can add more. Rather, haste sets a limit on the number of weapon attacks you can make with its Attack action. Hence, you cannot make both the normal attack and the Unleash Incarnation attack when you take the haste's Attack action, because that would exceed the limit of one weapon attack.
Moreover, the Unleash Incarnation attack is not some attack that occurs after the Attack action, nor is it separate from that Attack action. Rather, the Unleash Incarnation attack is part of the Attack action, so it's subject to the limits that haste imposes on the Attack action.
The above is the exact same reason why Extra Attack also can't exceed haste's limit. As a matter of fact, the relevant wording of Unleash Incarnation and Extra Attack are the same:
and