The biggest obstacle to growing zinnias successfully indoors is providing enough light. They require full sun which means at least six hours of direct outdoor sunlight each day. Outdoor sunlight is much brighter than natural indoor lighting, but there is a way around this. It will just take a little extra effort.
Zinnias are a popular annual in the flower garden. You can grow zinnias indoors if you grow them under fluorescent grow lights or in a greenhouse. Choose one of the many shorter varieties of zinnias so the pots won't topple as the mass of the top growth surpasses the combined mass of the pot and its soil. Zinnias will last for months indoors if you remove the faded flowers.