Hi Ea,
My style is very conversational. I'd be telling the story with lots of anecdotes plus photos. The book would cover some high spots, changes over time and meaningful moments in time reflective of the overall program. Think along the lines of a scrapbook - pieces that ring memory bells, interesting facts, some trivia. It would not be a comprehensive history of Scouting. It would be a celebration of the first 100 yrs with a collection of memorabilia.
An example that comes to mind is a link here where a Scoutmaster tells the story of a Scout in his troop who was in a wheelchair. That single story captures a lot about the program and what it can mean. Those few personal paragraphs would say more than page after page of recitation.
In talking about merit badges, I'd cover some changes over time. But, the central focus would be stories - like a Scout who earned every merit badge.
I guess it would have kind of a Chicken Soup feel but with more sidebars for info.