This book is for the Boy Scouts of America, and the flag it refers to is the United States flag.

I'm an American, but you chaps are living in British territory and you're British subjects, so you'll have to learn about the British flag or Union Jack, as it's called, for that's your flag.
"The Union Jack is the national flag of the whole British Empire.

The English flag was originally a red cross on a white field.

This is called the flag of St.George.Three hundred years ago King James the First added to it the banner of Scotland, which was a blue flag with a white cross, called St.Andrew's Cross, lying upon the blue from corner to corner--that is diagonally." Doctor Joe opened his travelling bag and drew forth two small flags, one the Stars and Stripes and the other the British Union Jack.
"I nearly forgot about these," said he, spreading the flags upon the table.

"This is the flag of my country," and he caressed the United States flag affectionately.