Flower Saver is a badge in Paper Mario and Paper Mario: The Thousand-Year Door that makes Mario's attacks cost less FP than normal. It costs either 6 BP or 4 BP to equip in each respective game. In Paper Mario, you can trade 25 Star Pieces to obtain it. In Thousand Year Door, you can find it at the Creepy Steeple, trade it for 10-Star Pieces to Dazzle, and you can steal it with Ms. Mowz's Kiss Thief from a Crazy Dayzee.
Multiple Flower Saver badges can be equipped at the same time, each decreasing FP costs by 1. However, the minimum FP cost of the skill will always be one, therefore you can never completely negate FP costs.