Non-standard English to Standard English, in Milne's Ugly Duckling
It is speech so it is not necessarily a proper sentence. So it is broken, and a run on sentence. She is in love and telling a story about her man.
Before the italics: Eg (her man) is an archer, but he is not really an archer. He just works in a support role in the armory.
Italics:
but old Bottlenose, you know who I mean, the Captain of the Guard,
The person in charge of the soldiers... (She calls him “old Bottlenose”)
says the very next man they ever has to shoot, my Eg shall take his place,
...says that when they have to execute one of the current archers, Eg will be given the open job for an archer. Then Eg will be a real soldier.
knowing Father and how it is with Eg and me,
Because the Captain (old Bottlenose) knows her father, and also know that she and Eg want to be a couple, but she has to marry a real soldier because she works for the Queen.
Paraphrase She’s in love with Eg and thinks he is great. Right now he is just a support guy in the armory, but she thinks he will be promoted to the fighting ranks as an archer when there is an opening. She cannot marry him until he becomes a real soldier. But she is gaga over him anyway and trails off telling a story about him.