I’ve just received this pattern so now I understand the dress and can join in with some suggestions.
Spots, stripes, gingham or even a plaid/ check (if you want to/ or are good at matching up patterns) would all suit this style and play down the girliness of it.
The idea of chambray/ light weight denim is good and with a constrast with mini piping or rick rack to break up the block of colour.
Monochromatic always works really well – blue and white, red and white or even black and white (white with a trimming of black). Very classic colour schemes.
It is certainly a pattern you could go wild with and have a number of them but all have them looking different.
Good luck with your choice. Whatever you choose I’m sure it will be perfect.