This name is a synonym of Linum flagellare (Small) H.J.P. Winkl..
The record derives from Tropicos
(data supplied on 2012-04-18)
which reports it as a synonym (record 50255048) with original publication details: Rhodora 66: 279 1964.
Full publication details for this name can be found in IPNI: http://ipni.org/urn:lsid:ipni.org:names:140813-2.
This name was in version 1 of The Plant List, record tro-50255048, and has not been changed.