Here is all I have been able to find. No where do I find that he was actually appointed a Brig. General.
The late General Flournoy. --The death of General T. B. Flournoy, of Arkansas, at Louisville, has been announced. He was a native of Kentucky, and for the last ten or twelve years a resident of Arkansas. He had received an appointment in the Confederate Army, and was, at the time of his death, making preparations to enter active service. The late General Flournoy. --The death of General T. B. Flournoy, of Arkansas, at Louisville, has been announced. He was a native of Kentucky, and for the last ten or twelve years a resident of Arkansas. He had received an appointment in the Confederate Army, and was, at the time of his death, making preparations to enter active service.
http://nlp.perseus.tufts.edu/hopper/nebrowser?id=flournoy%2Ct.%2Cb.&query=Perseus:text:2006.05.0237
.....
Arkansas troops for Virginia. --L. P. Walker, Secretary of War, has accepted Major T. B. Flournoy's regiment of Arkansas troops for service in Virginia, and they are instructed to rendezvous at Lynchburg, where they will be mustered into service.
http://nlp.perseus.tufts.edu/hopper/nebrowser?id=flournoy%2Ct.%2Cb.
.....
LITTLE RocK ARK
L. P. WALKER:
April 23, 1861.
Governor iRector, not being free as yet to send the regiment requested by tho Secretary of War, has placed in the hands of the undersigned the dispatch. "Will the President accept a regiment raised by the under- signed, complying in all other respects with the requisition of the Secre- tary?" Further, the governor has agreed to arm and equip the regiment when rendezvoused at Little Rock Arsenal.
T. B. FLOURNOY, Colonel.
JNO. B. THOMPSON Liet. Col.
W.N. BROUGNAH.
JAS. B. JOHNSON
http://history-sites.com/cgi-bin/bbs62x/arcwmb/webbbs_config.pl?md=read;id=23589
.....
Thompson B. Flournoy was a planter from Laconia, on the Mississippi River, and had been a supporter of the presidential ticket of Douglas and Johnson . . . .
Colonel Flournoy organized the first companies which arrived in Little Rock and sought admission into this regiment. Many of these initial companies had originally been organized as volunteer companies under the Arkansas Militia law which authorized each county to form, in addition to the standard militia regiment, up to four volunteer companies, one each of Rifles, Infantry, Artillery and Cavalry.[7] Units such as the DeWitt Guards from Arkansas County and the Jackson Guards from Jackson County had organized months earlier in the state militia as sectional frictions increased.[8] At the actual organization of the regiment at Little Rock on 6 May 1861, Colonel Flournoy was defeated for the colonelcy, and Captain James F. Fagan, of Saline County, was elected colonel; Capt. James C. Monroe, of Clark County, was elected lieutenant-colonel, and John Baker Thompson, major. Prof. Frank Bronaugh, of the military department of St. John's College, Little Rock, was chosen adjutant. Colonel Flournoy accepted the outcome with good grace; he was afterward promoted to brigadier-general in the Confederate service.[6] The unit was composed of companies from the following Arkansas counties:
http://en.wikipedia.org/wiki/1st_Arkansas_Infantry_Regiment