Man, trying to figure out the reading order for 'Claimed By My Brother's Best Friends' is a whole mood, isn't it? I swear, Alyssa and King's stuff feels like a puzzle sometimes. From what I've pieced together, you definitely want to start with 'Claimed By My Brother's Best Friends' itself. That's the core story.
After that, it gets a bit murky because there are spin-offs and alternate POVs floating around. I think there's one called 'His Forbidden Obsession' that follows King's perspective more closely, and maybe a shorter piece from Alyssa's view? The author sometimes releases bonus chapters on their Patreon or website that fill in gaps. The best advice I got was to just search the author's name on Goodreads and look at the 'series' page—it’s not perfectly organized, but the publication dates give you a rough guide.
I ended up reading the main book, then hunting down the extra scenes because I was hooked on the dynamic between the three of them. The order isn't super strict, but starting with the core novel keeps the initial tension and surprise intact.