Authors Doug Preston and Lincoln Child claim you can read their books out of order. But I read the last two books in this series first and am now reading the front half (I discovered the mystery authors by reading the last books first and am now catching up). Because I know what is going to happen, and know how the killer is revealed this book is less thrilling to me. So, I'd suggest reading the series in this order:
Brimstone
Dance of Death
Cabinet of Curiosities
Book of the Dead