Having a giggle at your dad, Em, and the french woman, Tory!
The only flat terries I've tried were babeco bamboo terry squares - they work well folded but tbh I find it really fiddly so they're mainly used as boosters (excellent in night nappies!) or as emergency back-up nappies.
I love bambinex terry squares. I love bamboo anyway as it's so soft but most bamboo nappies take ages to dry. The terries dry very fast. Also, they come in 75cm which is good as 60cm is too small for ds4 now so my beloved Bright Bots are too small.