Also! Which way should I display this? I don't know which end is up!
Note that your first two pictures show the reverse side of the signatures with all of the kanji appearing backward.
LIFE'S LOSERS NEVER LEARN FROM THE ERROR OF THEIR WAYS.
I feel that this flag is a made up representation of a hinomaru yosegaki, not a true IJA carried example. Although the "kanji" looks like kanji I have my doubts. It all looks to be done in the same hand as well, no variation in strokes size of character, etc. Also, the red sun in the middle is not proportionate to the flag, taking up a lot of space in the middle. The hanko stamps do look similar or are maybe the same as those on your referenced website, but I do not believe that they are for a shinto shrine. (also, in the Coll. Guild flag, why is the same hanko stamped more than once? -- I do not believe shrines or even well wishers, if using a hanko, would use a stamp multiple times on a flag. All that being said, there is the possibility that it may be a Navy Seabee created flag, which is becoming desirable in its own right. There are stories of seabees copying true flags and adding fairly legit. looking "kanji" to their creations. They also used the bottoms of buckets to make the sun circle in the middle of the white cloth to create the hinomaru. just my opinion.
Thank you so much for your insight. I've had some people who speak Japanese take a look at the flag via pictures online, and they confirm that the Kanji is authentic, but in an old fashion style. I hope to meet with the head of the Japanese language department at Vassar college soon for additional help.