Does Allah forgive one who swore to flee from war, while being unsure if he uttered that oath due to waswas?

Whoever doubts whether he swore an oath or not is not bound by anything.

Whoever swears an oath under the influence of waswasah (whispers/obsessive thoughts) is not bound by anything.

Whoever swears an oath to abandon Islam falls into two categories:

The first: If he is determined to abandon Islam, then he becomes a disbeliever immediately.

The second: If he ties the oath to something he wants to prevent himself from doing, such as saying: "If I do that, then I am absolved of Islam, or I am a disbeliever, or a Jew, or a Christian." This person does not become a disbeliever, because he dislikes disbelief and wants to prevent himself from doing something. However, if he does the thing he swore an oath about, he is bound by an expiation for breaking an oath (kaffarat yameen).

As for swearing an oath to commit forbidden acts, like fleeing from jihad, committing zina (fornication/adultery), or drinking alcohol, he is sinful for committing the act and must repent from it. He should also pay an expiation for breaking an oath as a precaution, but he does not take the ruling of someone who commits forbidden acts.

However, whoever utters a word of disbelief definitively, or ties it to a matter without intending it as an oath, becomes a disbeliever immediately.

As for the one afflicted by waswasah, there might not even be an oath in the first place. If there is certainty of the existence of this oath, then repentance and the expiation for breaking an oath are obligatory.