Although there are no longer any hard and fast rules about who pays for what in a wedding, tradition dictates that the bride's family pay for the ceremony and reception flowers, the bridesmaid bouquets, the flower girl flowers, the groom's boutonniere, and the cake flowers.
The groom's family pays for the bride’s bouquet; the boutonnieres for the groomsmen, fathers, and grandfathers; and the corsages for the mothers and grandmothers. Traditionally, the groom's family also pays for the rehearsal dinner and would thus be expected to pay for any flower arrangements they decide to have there.
But Times Have Changed, Haven't They?
You don't have to follow the flower cost breakdown exactly. For example, the bride's parents might have already offered to cover the cost of flowers. Asking the florist to split the bill up between the bride's flower costs and the groom's flower costs comes off a bit gauche anyway.
Before anything is set in stone, sit down as a couple and estimate what you'll spend on the big day. Choosing an ideal reception site first will help dictate the rest of your budget, as it will likely make up the bulk of the expenses. If you know there's a certain photographer you want to use or already have your dress picked out, then, by all means, include those items in the expense list. You can certainly make other general decisions about the wedding, like the theme, where you'd like the ceremony to take place, etc.
Talk to your parents and explain what you already have in mind, and graciously ask them if they're willing to help out with any costs. As previously mentioned, if the bride's family has flowers covered, then the groom's family doesn't need to worry about those details. However, they should be contributing financially in other ways, like with food, entertainment, transportation, etc.
In this day and age the bride's parents shouldn't be expected to foot the bill for everything. You could also split the budget evenly. The bride's family, the groom's family and the bride and groom each assume a third of the costs.