Here is the original watercolor :
link
The watercolor was exectued in 1817, when finding flags of Napoléon for a model to hold might have been difficult.
The work is attributed to Eugène Louis Lami, but signed just "Eugène". I am not so sure : the young Lami would seem to have a different style and signature, compared to his mature works.
In 1817, Lami was a 17-year old assistant to Carle and Horace Vernet, and they were preparing a set of 100 lithographs "Collections des uniformes des armées françaises de 1791 à 1814", which was published in 1821.
link
The original watercolor has no known original title. It appears to have been aqcuired by the Brown collection from a New York print dealer in 1949, along with other 19th century European works.
The attribution "2nd Foot Grenadiers" is not consistent in the various editions of the Lachouque. "1st Grenadiers" and explanation about the flag's design can also be found :
link
The editions of the Lachouque as far as I know ….
English, translated by Anne S. K. Brown :
--- 1st Edition : 1961 Providence, Brown University Press & London, Lund Humphries
--- 2nd Edition : 1962 Providence, Brown University Press & London, Lund Humphries
--- 3rd Edition : 1978 New York, Hippocrene Books & London, Arms and Armour Press
--- 4th Edition : 1997 Pennsylvania, Stackpole Books & London, Greenhill Books & Singapore : MRM Graphics Limited
--- 5th Edition : 2017 London, Frontline Books
French :
--- 1st Edition : 1945 Paris, self-published
--- 2nd Edition : 1956/1957 Paris, Bloud et Gay & Tournai, Desclée
--- 3rd Edition : 1982 Paris, Lavauzelle