Type of motor
As jsotola has mentioned, you are probably looking for a micro servo.
Something like a Tower Pro SG90 (weighs 9 grams):

Or maybe even smaller.
The size and power of the servo that you will require depends upon your design:
If all of the petals are connected, via some mechanism, and they are all meant to open at the same time then one servo will probably suffice.
However, depending upon the load of all of the petals and the material that they are made of, i.e. weight, you may require something more substantial, like a MG995 or MG996
If the petals are to open independently, then you would probably need a servo per petal, which would increase the weight (if the servos are mounted next to the petals up on a stalk), and so maybe something smaller than a SG90 would be required. Obviously, if the petals are connected to the servos via a rod, and the servos are mounted in the base, then weight will not be such a major factor.
Control mechanism
You don't say whether you have the controller already figured out, but in case you do not, then you'd probably want something like an Arduino with a servo shield, and then a simple sketch running on the Arduino that just sweeps the servo arm from side to side.
For what it is worth, a previous post of mine, Overheating/Jamming MG996R servo, shows the Arduino shield and a sketch that provides a simple sweep action.
However, there are loads of example out there, and the Servo library (by Michael Margolis) for the Arduino IDE even comes with an example sketch (actually a suite of examples) for servos.
However, this is beyond the scope what you asked (just about the motor), so I will not elaborate.