A fluid material dispensing kit including a pouch, provided with a flexible casing and a dispensing case provided with a cover that is to be mounted onto a base. The cover includes an upper recess that has a manually flexibly deformable wall mounted thereon. The wall has a dispensing opening, and the cover is provided with a lower reinforcement that defines, with the wall, a pumping chamber. The reinforcement has a supply opening. The distribution opening and supply opening are provided with, respectively, an output valve and an input valve. The pouch has, built therein, a coupling provided with a well that is sealably covered by the casing of the pouch, and the reinforcement includes a nipple that is to be placed into the well. The nipple is set up so as to enable the perforation of the casing during the placement thereof into the well.