If your flowers are annuals, you can wait until Fall and cover the whole bed with black plastic, then a layer of mulch or straw (for aesthetic effect). In the Spring, rework the soil and add compost, as most weeds dislike loose, rich soil. Replant the flowers, and if any of the weed comes up, pull it while it's very young. One of the reasons that gardeners like to plant in neat rows and label the rows is so they can easily figure out what belongs in the bed and what does not, even when all of the plants are in their infancy.
If your flowers are perennials, clip the weeds very close to the ground. Push cans all the way into the soil where the root of the weed is, hammering them in if you have to. Small cans that tomato paste comes in work well for this. Leave the cans in the ground, adding more where you see more weeds, for at least one growing season.
With any weed, you can experiment with lime and vinegar. All plants have a soil acidity level that they prefer. Acid-loving plants will wither if you apply lime. Plants that do not like acid soil will wither and often die with a generous application of vinegar. Try vinegar on one plant and lime on another and see what happens.