Answer: I should start by mentioning that if your flowers are well adapted to the growing site and are healthy and growing well, you may not really need to control the moss at all. Moss in and of itself is not harmful and in some cases can be very attractive when combined with plantings.
Moss usually grows in locations where the soil is compacted and/or drains poorly and/or is extremely acidic and/or is quite infertile. To remove the moss permanently, you would have to change the soil environment by methods such as aeration, adding organic matter, and/or adding lime to raise the pH. Any of these would potentially affect the flowers.
For a more gradual approach, you could begin by testing the soil to check the fertility and pH and correct those slowly over time. (Do not lime around plants that require an acidic soil.) Also use annual topdressings of good quality compost along with a constant layer of organic mulch. These will help feed the soil slowly over time as they break down. You may also be able to aerate slightly by plunging the tines of a garden fork into the soil between your flowers, being careful not to damage their roots.
I hope this helps you evaluate the situation.
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