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The 3D aspect of most objects other than faces is best revealed with back rim lighting to define the overall shape and lighting in front which provides enough "fill" for the camera to record the shadow detail but also with a downward "key" component to model the front side. The fourth ingredient in the lighting "recipe" is the background / foreground contrast which is a function of the color of both and how they are illuminated.
For a natural look in flash lit shots take your clues from nature. These shots were taken with natural light with flash assist in front:
These indoors with a pair of flashes:
They all have the same basic lighting strategy.
Outdoors I put the sun behind the subject and adjust exposure until the parts it hits are below clipping using the clipping warning of the camera (making correct exposure a no-brainer). Exposing for the highlight detail makes the front side which is naturally lit by the skylight too dark because the sensor range can't handle the contrast . That's why adding flash in front is necessary outdoors if a full and normal "seen by eye" range of detail is desired..
The "trick" to making the flash on the front side look natural is to pay attention to where the natural skylight comes from that is filling the shadow side your eyes are looking at. It is not "flat" fill light coming from the camera axis! Skylight models the object from above with very soft diffuse low ratio lighting because more light comes from directly overhead that "wraps" around the sides.
So when adding a single flash to the front side to deal with the contrast the camera can't handle you don't want it level with the camera axis you want it to have a natural downward direction like the skylight if you want natural looking results in the photos . By raising my flash on a bracket and using a diffuser on top of it I move the center of my frontal flash 16" above the lens axis:
It might look strange and cumbersome, but that's what is needed to achieve more natural looking results with flash. It's not rocket science you simply need to observe how natural light illuminates things, observe how some directions of light make objects look 3D and others make then look flat in 2D photos, and follow those clues when placing the flash which creates the modeling in the photograph at similar angles.
Fill is a technical issue. If the camera had a 15 stop range you'd never need fill flash. In open shade or an overcast day you don't need it because the flat (contrast) lighting allows the scene to fit the 8 or so stops of light your sensor can record with detail. So whenever a scene range exceeds sensor range you need a fill source to lift the shadows.
Outdoors using the sun as the "Key" or "Rim" lighting to create the highlights from front or back a single flash can be used on the front side. But if the flash is down near the camera lens the results will look dimensionally flat and flat in terms of lighting ratio because the flash will cast no shadows and overpower any modeling the skylight was creating. Moving the flash up away from the axis on the bracket (or a stand) causes it to create shadows the camera sees. So it's role and function changes from "fill" (even illumination / no shadows) to "key" (frontal modeling).
Where does the fill come from outdoors? The skylight. Do you have any control over the lighting ratio via the tone of the shadows? No, not with one flash in front. That's why outdoor shots with a single off axis flash in front will have dark shadows. The only way to get them lighter is to change the overall exposure, but that will blow the highlights. The solution? Use two flashes in front: one to create the modeling from off axis and a second to add "neutral" shadowless fill and control the lighting ratio.
So ideally to make a flower look 3D you'd want three light sources:
rim light from behind to define overall shape and separation with the background
fill light to allow the camera to record shadows detail at the f/stop you select
key light in front to model the 3D shape on the side the camera sees
If forced to use one flash outdoors raising the flash to make it a key light and create modeling isn't the ideal solution but it produces better results than putting it next to the lens and destroying the natural modeling. Where do you want to put it outdoors? Observe the direction the skylight is casting it's subtle shadows on the front side and put the flash where it creates shadows the same direction. That will also put the highlight clues in the same natural looking places as the skylight was before adding flash.
When you move inside you need to remember the angles the sun was hitting the back side and the skylight modeling the front side and duplicate those angles with the back rim flash source and the frontal key source.
Indoors you will not have the skylight for fill so you will either need to bounce a lot of spill off the ceiling and walls to mimic the skylight from your rim and key lights, or use a third flash as fill. That's the better option because it allows independent control of the shadow tone.
What if you only have two flashes? Do the same as outdoors with one flash: put one behind to act as "sun" and put the second in front, but above the subject to create modeling and fill at the same time. When I designed my DIY diffusers seen in the shot above I made the top flap hinge so when using single flash indoors I can open the flap and bounce light off the ceiling and forward at the same time, which creates frontal lighting very similar to skylight indoors of the room has a low white ceiling. When there isn't a ceiling to bounce spill fill off of I get the modeling from the fact the flash is raised off axis but know I'll get darker shadows.
This is a two speed light still life test:
These are the same objects photographed with four studio lights:
The two extra "ingredients" in the lighting strategy were the independent fill source to control the shadow intensity so the camera could record more detail and the background light making the black background gray so there would better foreground / background contrast and a lighting created vignette to guide the eye inwards.
This information should give you some ideas how to improve your shot. You may also find these tutorials of mine helpful:
Creating 3D in a 2D photo: http://photo.nova.org/Creating3D/
Using the four ingredients to create it: http://photo.nova.org/FourLightExercise/
Lighting soft texture objects with "hard" light: http://photo.nova.org/Fur/
The last one is oriented more to shooting pets, but flower petals present the same challenge of rendering in the 2D photo the texture seen by eye in person. The clues come from contrasting highlights and shadows and with soft objects direct light is what is needed to reveal texture realistically. So experiment with direct flash and compare the result with what you get with diffusers. You'll discover you get more "pop" with small or direct sources than big diffuse ones used for portraits where the goal is hiding blemishes and texture (wrinkles).
On flowers it's the specular highlights which enhance the illusion of 3D similar to direct sun hitting it: