Instead of waiting for flowers to arrive at the shop, go to the island and sign up for a tour.
I like to go on Hide-and-Seek Beginner's Tour, because it's so easy that you can get 7 medals while running around collecting flowers.
After collecting the flowers, it remains in your inventory, which you can then put into the box to bring to your village!
Basically, this saves time for you to wait, and has a never-ending supply.
Technically, you can't call it cheating
TL;DR: Steal flowers from tours
I like to go on Hide-and-Seek Beginner's Tour, because it's so easy that you can get 7 medals while running around collecting flowers.
After collecting the flowers, it remains in your inventory, which you can then put into the box to bring to your village!
Basically, this saves time for you to wait, and has a never-ending supply.
Technically, you can't call it cheating

TL;DR: Steal flowers from tours