Flowers are the start, the note is the point
Missed anniversaries, harsh words, a forgotten pickup. Everyone ends up needing to say sorry at some point. Flowers can help, as long as they come with an honest note and not just a signature.
Soft colors usually fit an apology better than loud ones. Pink, lavender and white feel gentle. If the person has a favorite flower, use it. It shows you paid attention, which is often what an apology is really about.
If the apology is to a partner, our romantic flowers page has more ideas. If it is to a friend or coworker, a small arrangement is better than a huge one.