WW2 Flag help

Hello,
I have what looks to be a 'diary record' of a soldier's wartime movements in China, written onto a national flag. I have been able to translate the dates but some of the cursive type kanji is making it quite difficult to decipher.

Any help would be greatly appreciated. Many thanks in advance.

This is what I have so far...
1937, August 22. = 昭和十二年八月二十二日

1937, August 29. =

1937, September 14. =

1937, October 17. =

1937, November 2. = ナ途碼へ迫写 ??????

1937, November 20. =

1937, December 2. =

1937, December 4. =

1937, December 5. =??入城

1937, December 11. =??入城

1937, December 14. =??入城

1937, December 15. = 日陽入城 = Nichiyo entered the castle?

1938, 5. = ??入城

1938, June 13. = ??あ虜入城

1938, August 9. =?? 湖ロ入城

1938, August 25 =.呉る入城 = Gol entered the castle ??

1938, October 29. = 漠ロ入城 = Hiroshiro entered the castle ??

1939, March 25. = 呉城入城 = Kure-jo entered the castle. (Maybe Kure?)

入城 means "entered the city" (basically conquered, then entered the city). So any characters before 入城 refer to the actual city or area that was conquered. Presumably you could find a map of China with the old kanji characters for the place names, and pick out the place names by looking at the map. Usually these things are given before the soldier goes off to war. This one would have had to have been presented after all those movements took place, so it couldn't have been a diary unless the person writing knew beforehand exactly how much space he would need at the bottom of the flag to fit all those movements in.

Thank you Majestic. I always thought the term given to these types of flags was a bit erroneous but for a lack of a better term I went with it.

Your map suggestion is quite clever and I may just have a map that could help, but trying to match printed kanji against some of the 'cursive' types has undoubtedly been my undoing, as not having an intimate knowledge of the language, has lead me to make questionable guesses as to which character is which, hence why the call for assistance.

Again, thank you for your time in replying to my query.

Maybe this will help you get started. From right to left, some of the cities are
鎮江
？慶
湖口
星子
漢口
呉城
There are 4 other cities that I couldn't pick out. Before the cities, the entries refer to other actions. I'm starting to think this isn't a record of one person or one platoon's achievements, rather it is recording the Japanese army's achievements as a whole.
And, I hate to be a buzzkill, but you cannot completely discount the possibility that the flag is a fake. Having said that, there is nothing in this flag that jumps out at me as fake. But it is curious as to why this sort of record would be on a flag like this. Anyway, be that as it may, good luck in deciphering the other cities.