I would like to grow my own garden of edible flowers

I would advise you not to proceed with this setup as due to the extreme heat produced from a heat lamp, and the lack of adequate air circulation in a closet, you are creating a fire hazard.

There are special lamps for indoor terrariums. These are called Grow Lights. As plants require UV (ultraviolet) light , these lamps attempt to provide a light spectrum similar to that of the sun, or appropriate for photosynthesis to occur.

Heat Lamps are a special type of lightbulb that emit infrared heat radiation, heat not light. These are commonly used in chick hatcheries, in a bathrooms without central heating to warm up the room.

atleast 7 hours of "sunlight" per day

You're welcome.