James Kochan is worth quoting on the subject of flank companies in the federal infantry regiments:
"Under the command of Eleazer Ripley the 21st Infantry evolved into a superb regiment that usually lived up to its colonel's high standards. When the elite flank company of light infantry disgraced themselves in a riot in May 1814, the now-BrigGen Ripley dissolved it and all other light companies in his 2nd Brigade of the Left Division, replacing them with a second grenadier company per regiment. The grenadiers were distinguished from the battalion companies by two chevrons on the upper right arm, red-tipped pompoms on their caps, and the practice of always wearing their overalls under the knee-length gaiters rather than outside, as worn by the rest of the companies on campaign. Grenadier sergeants alone were entitled to wear boots in lieu of gaiters, at their discretion. One honour accorded to the grenadiers was to escort the national standard . . . and regimental colours from the parade."
Kochan and Rickman, THE UNITED STATES ARMY 1812-1815, Osprey, 2000, p. 44, note C3.
This confirms not only the existence of both flank companies as regular practice (at least in the Left Division), but also the pattern of distinctives for the grenadiers. I haven't found a direct reference for the light company, but I use a green plume and yellow cord as Rickman shows for the rifles as my best guess.
One of the problems with inferring how the infantry battalions were organized internally is that, as Rudy noted, the sources simply don't go to that level of detail. I have found it is just as true in accounts of battles in the various Northern theaters.
But we can learn more from available orders of battle (OOBs). The largest concentration of light infantry I have found is provided by Fitzhugh MacCrae on the Histofig website
link
He notes that James Gibson's 4th Brigade of the Left Division consisted of 5 companies each of the 1st and 4th US Rifles, and the 26th Infantry Regiment. MacCrae notes that the 26th was a light infantry regiment in 1814. Kochan states that the unit was uniformed and armed as Rifles (p. 20) in 1814.
As a side note, Kochan also notes (p. 46, note G2) that the Light Artillery occasionally served as light infantry when they were fielded in an infantry role.
I also recommend consulting The Nafziger Collection of orders of battle at the Command and General Staff College web site to get a fuller idea of how light infantry and flank companies were distributed.
cgsc.edu/carl/nafziger.htm
Nafziger's 5 June 1813 Stoney Creek OOB (813UFAA), for example, lists 1 company of rifles and 3 companies of light infantry present with the US forces, citing Armstrong's NOTICES OF THE WAR OF 1812, 1840.
An even more interesting example is his 31 July 1813 OOB for the New York Militia in Mooers Division (813UGAC), quoting Crawford's PUBLIC PAPERS OF DANIEL D. TOMPKINS, GOVERNOR OF NEW YORK 1807-1817, 1898. The Division included "light infantry, grenadiers and riflemen" detached from their parent militia regiments. This confirms that the New York militia also had flank companies.
His 14 July 1814 OOB (814UGAA) lists detached companies of the 1st US Rifles with the 6th District (North & South Carolina, and Georgia) and the 9th District (Right Division). The 24 August 1814 OOB for Bladensburg (814UHAD) lists companies of Navy Yard Rifles, Baltimore Rifles (Maryland state militia), and James City Light Infantry (Virginia militia).
One observation: the listings of detached rifles and light infantry companies in the brigades are not sufficient in number to account for all the flank companies, so I conclude that it was not a universal practice to detach the light infantry. My suggestion is that the American practice was more like the then current British or French practice, than the earlier practice in the American Revolution.
Both vtsaogames and Rudy noted the prevalence of volunteer units (foot and mounted) in the Southern theaters to serve as spies, scouts, and skirmishers. Not surprisingly the OOBs lack mention of detached federal rifle and light companies, unlike the practice in the Northern theaters. Though not direct confirmation that such detachments didn't occur, it at least supports the idea.
Rick