You have a lot of options actually
1. Start with your most basic ones, which are social platforms. Advertise, promote, SEO, reach out. This gets the ball rolling quick for new sites with a competitive niche like this
2. Content creation and marketing - create an infographic, start an epic storyline post or whatever that your target market would like. Segment them first. For example, there's a good chance someone looking for the service is dating someone. Why not create a content piece about the best ways to impress a girl he's dating with things he can do along with a "surprise" flower delivery.
3. Promotion and contests - maybe you can do a weekly special, like customising certain products for the receiver.
4. the usual SEO - this is probably the longest in terms of ROI but it's the most important long term.
There a lot more you can do which is limited to your imagination and budget. I know other mozers here have other creative or traditional things in their mind that will also help a lot. 