Women's character shoes are named as such since many actresses in the theater use them while performing "in character". Made by almost all dance brands such as Capezio and Bloch, character shoes are used mostly in theater-type dancing and can be used in beginner lever Flamenco classes. These shoes are basically dance shoes (usually with a low heel and a Mary-Jane or T-strap) with a leather sole. They can come in a variety of colors, but are sold mostly in tan, white or black.
Used in the traditional "Flamenco dance", Flamenco shoes are shoes that appear relatively similar to character shoes. Most of the shoes have a low heel (under 4 inches), however you can purchase them at almost any height. Practice Flamenco shoes are usually tan or black in color and have a Mary-Jane or T-strap buckle. The important difference between character shoes and Flamenco shoes is that Flamenco shoes often have nails at the bottom of the shoe to produce an authentic "Spanish sound".
The short answer is no. While character shoes can be used as Flamenco shoes for the beginner who has not decided to invest in an expensive pair of Flamenco shoes, Flamenco shoes are not interchangeable for character shoes. It may be possible that a director of play may require an actress to wear Flamenco shoes for a certain scene, but it is not a good idea to try and dance in Flamenco shoes for a non-Flamenco dance class. The nails at the bottom of the soles will be extremely loud and possibly damaging to the floor you are dancing on.
While character shoes are usually used for dancing in classes or in a theatrical play, taps can be attached to them for tap dancing. However, this is permanent, so do not plan to use one pair of character shoes for both your character shoe and tap dancing needs. The taps can usually be attached at your local dance store. If not, they can recommend a cobbler who will be able to attach them.
Character shoes are available at virtually any dance store. Flamenco shoes may take a bit more detective work to find. You can custom order Flamenco shoes online or you can ask your local dance store where they recommend you purchase Flamenco shoes. You can also ask your dance teacher where she recommends you make your purchase. Many Flamenco products are imported from Spain, so they may run a bit more on the expensive side than character shoes.