This name is a synonym of Phlox glaberrima var. triflora (Michx.) Reveal & C.R. Broome.
The record derives from Tropicos
(data supplied on 2012-04-18)
which reports it as a synonym (record 50175208) with original publication details: Bartonia 23: 5 1945.
Full publication details for this name can be found in IPNI: http://ipni.org/urn:lsid:ipni.org:names:193404-2.
This name was in version 1 of The Plant List, record tro-50175208.