Yes you can! I was wondering the same so I ran an experiment with a noob char. And this is what I did:
-First of all, I bought 1 backpack of Kitchen Knives cause I know when you cut the flower it consumes the Knife.
-After taking the flower I headed back to Bozzo, and used the words: Lost, Repeat, Mission-no. And pretty much every keyword I could remember from other quest NPCs that allow you to repeat quests or take more than one item, also tried putting the flower away, as in not carrying on my backpack while talking to Bozzo. To my dissapointment, none of those worked.
-I decided to go back to the White Flower temple and log out next to the flower so I could set a counter with 20 and 24 hours to see if it had any kind of cooldown. To my pleasant surprise, I was just curious and put the flower I already had on the floor and used another kitchen knife on the white flower and IT GAVE ME ANOTHER ONE! It was just right after and I was hyped so I tried again and again with the flowers now inside the backpack and it worked aswell. So, yes! it is possible, It has no cooldown, you can take as many as you want, and you only need to have several kitchen knives on your backpack for each white flower you wanna get. Here is a screenshot of me getting them.
-You can get limitless flowers ONLY if you don't complete this mission. It won't work on a character that already does.
-Its an easy to get item as you can start "What a Foolish quest" at any level and this is the first mission of the quest.
-It only requires 1 Kitchen Knife for each flower you want to get, Kitchen Knives are sold at Chephan (Western Venore Shop) for 10gps each.
-These flowers can be traded on the market.