The flower spawn has been updated as of August 1st 2017. All the information online is not reliable, do not believe any of them. The only information that is supposedly credible is from the patch notes:
That being said, the 4 spots the flower spawns is not known. There is a post that shows it in the Swordsman section of this forum, but in my experience (picked flower August 17 2017) the flower spawned right behind my character behind the mango. Could be coincidence or that the spot is one of the 4 possible spawn points.
Some tips I can offer everyone is to first choose a channel with no one in it. Start from character select screen and remember the time. Then, set a timer on your phone or computer for 14 minutes. Every 14 minutes, run around the spawn area and search to see if the flower has spawned in the 4 spawn spots. You should get it soon as long as no one has taken it when you were away.
I started at 12:24 pm and found my flower at 3:52 pm. There is no 4 hour respawn or whatever - none of that information is verified after this patch and you shouldn’t believe it. Just know that the flower stays spawned for 15 minutes and supposedly it won’t disappear after someone picks it.
The thing is, when I picked the flower, I cancelled the action. After picking it on my second attempt, it disappeared. Either the mechanic is that the flower will stay spawned for the 15 minutes as long as there is a player who has not yet picked the flower is on the map, the 15 minutes just coincidentally happened to be up right after I picked it, or the patch notes is misleading. It may only be a two time thing. I don’t know.