Yes it does. As long as it has a symmetry without rotation. If you do the rotation either way it does have symmetry. :)
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Flowers display a number of forms of symmetry, reflection, rotational etc. You need to be more specific regarding what type of flower you are asking about.
No a Z doesn't have a rotational symmetry
A trapezoid has no rotational symmetry.
It has line symmetry (straight down the center) but not rotational symmetry.