Are those Kamikaze planes?
There were multiple kinds of planes used in kamikaze attacks, so the literal answer to your question is “we don’t know what the mission is.” (Unless Nathan wants to tell us.)
The planes are generic enough that we could interpret them as Allied planes flying over Japan – but my reaction was similar to yours, that the cherry blossoms imply the planes are in the WWII Japanese air force.
I’d say the wing markings make it rather definite that we’re talking about Japanese planes. Looking at the cockpit and the tail, I’d guess a Mitsubishi Zero.
The characters in the pink panel are Japanese, so I think there’s little doubt about the nationality.
My Japanese skills are terrible, but I think it’s something like koori too ni, literally “to the distant ice”. Which ought to be enough of a clue to trigger a memory of a movie with an old Japanese man remembering planes, a girl, flowers, a polar expedition — but I got nuthin’. My initial response was Miyazaki’s “The Wind Rises”, but that doesn’t seem like a good fit.
(And nice job drawing the kanji, by the way. Seems like they’d be hard to copy if you haven’t studied them.)
The Japanese is ‘eien ni’, meaning ‘for eternity’ or ‘forever’.