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You're supposed to rotate it 90 degrees counter-clockwise.
As the image appears, the words at the bottom (supposed to be right hand side going up to down) is "Prayer/Hope for continuing/long lasting military fortunes"
The words surrounding the sun seem to be names, though the marking at about the 12:30 mark (between 12:00 and 1:00) is "mother and son". Plus at least two of them seem to be feminine names, so I'm guessing those are not the name of a soldier's brothers in arms.
I don't suppose you know the circumstances that your grandfather acquired the flag in.
EDIT: Taking a stab at the names themselves (I'm not 100% sure here), going clockwise from 12:00 as the image appears
Kimura Ichita/Itta/Kazuta (or any of a bunch of other pronunciations used for the name)
mother [and] son
Nakamichi Reiji
Gaien Taiji
Nonbei (no family name given)
Can't read the one at 8:00
Kobayashi Michiko
Ambassador Kurusu (Cruz? A foreigner?)
Yamada Anko (I think).
If it’s something you’re willing to do, you could try to track down the surviving family members of the soldier and return the flag. It really means a lot to the families and gives them closure.
Just an addendum question for anyone who is knowledgable about WWII Japan:
One of the signatures seems to be of a クルス 大使 (Ambassador Kurusu). Is it actually referring to Ambassador Saburo Kurusu? (I am not sure if people are in the habit of signing themselves in Katakana)
Do officers and diplomats sign these good-luck flags?
Hey, I do not want to discourage anyone from giving any answers to this question, but you might want to head to the subreddit r/translator where many people have been there with the similiar issue so it would be much easier for you to get an answer there.
Disclaimer, I am not trying to advertise this subreddit in any way I decided to put the link just to help you out.
Looking at the writings, these are names signed by different people. Perhaps they were signed by people from the soldier’s hometown. “Mother & son” is written next to one of the names. I would assume that it was a man signing it on behalf of his family.