There isn't any herbicide which will not kill the flowers too, except ones formulated for use on grasses. Anything which will kill broadleaved weeds will kill all other broad leaved plants. Hoeing, hand weeding with a fork and mulching will all help.

You: pull. Dig. Mulch.
Set a regular schedule. Say once a week.

The best "weed" killer for an organic grower would be mulches and cultivators. There are no organic sprays that will kill unwanted plants and not those we want to grow.

If you have pics of the specific weeds, I think more suggestions could be given. For example, nutsedge may take a different approach than dandelion.

Agreed. Boiling water for some things, smothering for some things, mutilation beyond recovery for some things, digging as a last resort (a matter of my opinion - some people would prefer shovel first.) If there was one quick, general answer to your question, there would be no need for this forum. Come on back with more specific questions!

Weeds are so much easier to pull in loose, healthy soil. Are your weeds hard to pull?