You working with the file where there is no overlapping. Select all the flower elements corresponding to the Rigid Body Active type, leaving one of them selected as active element. From now on you should work that way leaving the elements selected:
From Object Menu, Set Origin → Origin to Center of Mass (surface). From Object menu, Apply → Scale. From Object menu, Relations → Make Single User → Object Animation.
From the Physics Properties Tab, in Rigid Body set Shape to Mesh. Right Mouse Button (RMB) on that Mesh field, and select Copy to Selected. In Sensitivity item, set Margin = 0.01 and RMB and Copy to Selected.
In the Scene Properties tab, in Rigid Body Settings you play with small values in Substeps Per Frame (e.g. = 2) and Solver iterations (e.g. = 5). And you increase the Speed to ~ 1 or 2.
Now, maybe you need keyframe “Dynamic” property in Rigid Body settings of the petals in each layer of three petals starting from outside to inside, with approximately 5 to 10 frames of difference between each layer. Dynamic disabled up to frame 175, and Dynamic enabled incrementally from frame 175 for each layer of three petals (for example the first outer layer of 3 petals with Dynamic enabled from frame 175, the next layer of 3 petals with Dynamic enabled from frame 185, and so on until the last inner layer). To work comfortably, Hide in viewport the layer of petals in which you have already set keyframes. Also you disable Rigid Body World in Scene Properties tab until you finish the job. This can be a bit tedious to do.
By the way, I think Soft Body would be more suitable for this kind of simulation. But it is too heavy to process in Blender and I have no experience with it.
Remove collision of “TIGE” object and set Rigid Body “Passive” type.