Naturally Speaking

Albinos and partially white members of most species attract more attention than the pigmented forms.  White coneflowers, although not completely white plants, have white ray flowers around the edge of a composite head or inflorescence. 
Remember, a sunflower-like bloom is an assemblage of many flowers, most of them quite incomplete and lacking some of the regular flower parts.  There are thousands of tiny flowers in these heads, sometimes arranged to give the appearance of a single, huge bloom.  What an interesting way to dupe pollinators, and us, as to what's going on here.
The disc flowers in the center of a coneflower head are usually not white in the plants with white ray flowers.  Of course the stems, leaves and roots of these plants are not white either. 
True and complete albinism is difficult to imagine in a plant, one who gets its power by absorbing sunlight with green pigments.  There may be such abnormal coneflower plant but the plant would not live beyond the seedling stages.  It would have no power to grow beyond what's in the seed that germinated.
Some albinos, including mostly white individuals, are protected.  Wisconsin's albino and white, white-tailed deer are examples.