Calcite is a flux stone; however, it is not particularly special as it is found solely within limestone and marble, both of which are also flux. Its only distinguishing characteristic is that it is a magma-safe rock (which you should already have in abundance).
 In Real Life
Calcite is a crystalline form of Calcium-Carbonate (CaCO3). Calcite is extremely common, forming multiple types of rocks, such as limestone, marble, and chalk, it is also known to form as a concrete in some sandstones and siltstones. Calcite, along with other crystalline forms of Calcium Carbonate such as Aragonite (which is not present in Dwarf Fortress) is readily edible (although not easily chewed, and not very palatable), and can be used as a supplementary source of calcium in an otherwise calcium-poor diet.
main constituent of limestone, but can be found as crystal