I did a deep dive on google just to see if I could find anything that came close to matching this. It's a long shot, but maybe Finding Mighty? No mention of magic, but it's got brothers, parkour, a girl, a necklace (close to an amulet?), and is a blue book: https://www.amazon.com/dp/B01MF8NDFG/ref=dp-kindle-redirect?_encoding=UTF8&btkr=1
I did a deep dive on google just to see if I could find anything that came close to matching this. It's a long shot, but maybe Finding Mighty? No mention of magic, but it's got brothers, parkour, a girl, a necklace (close to an amulet?), and is a blue book: https://www.amazon.com/dp/B01MF8NDFG/ref=dp-kindle-redirect?_encoding=UTF8&btkr=1