White is such a difficult colour to photograph, Kim.
#1 fails for me due to the background problems. But #2 looks reasonable.
Whilst it is always better to err on the side of caution with white subjects I suspect you can get away with just a fraction more brightness.
I can't see the shooting details on these images. But I would have used Aperture Priority and probably somewhere around F8 to F14 range. Some exposure compensation is usually required on very pale, or very dark, subjects.
Flowers often photograph better under slightly subdued lighting as opposed to bright sunlight which can cause over saturation in some brighter colours.
Really...I didn't know that...I must be a terrible photographer.I do not recommend going into Photoshop or doing B&W conversions (that's a thing many people do without knowing how to expose or compose properly first).
For me, the second posted image (red) is worse. But you were probably on a hopeless task right from the beginning.
Flowers, are difficult; and unless you get the light correct at the time of shooting you are destined to failure. Which is what happens to so may of my botanical images!
Over saturation of a particular colour is always a risk and under exposure needs some careful editing during processing.
Besides white, red and blue flowers are always tricky; and yellow is never easy!
But don't give up - keep experimenting with the light when shooting. Eventually you will get the knack of producing good results everytime. Sometimes I use a piece of white card, or something similar, to reduce bright direct light; or to reflect more light onto dark areas.
Whether to use flash is debatable and tends to depend on the reflective surface of the flowers.
A tripod certainly helps but, even then, wind movement can easily move your subject out of focus.