This information comes from the Regimental History of the Royal Irish Fusiliers which also shows a photograph of the flag, this is, I believe, in the National Army Musuem, London.

THE MONTE VIDEO FLAG

Sir Charles Oman describes the quarterings of the flag as:

1. The small central shield gives the Arms of Spain proper, being 1st and 4th quarter gules, a castle or for Castile. 2nd and 3rd quarters argent, a lion rampart gules, for Leon. In the point of base a pomegranate proper on a field argent for Granada. Over all an escutcheon of pretence of France, viz., azure three fleurs-de-lys or, for the reigning dynasty of the Spanish Bourbons.

2. The minor quarterings arranged round the central shield are: [counting from the upper left-hand corner]

a. Paly gules amd or for Aragon.
b. Party per saltire, the upper and lower quarters paly or and gules, the two lateral quarters argent, an eagle displayed sable for Naples and Sicily.
c. Gules a fess argent for Hapsburg Austria.
d. Azure, semee of Fleur-de-lys or in a bordure gules and argent for the Duchy of Burgundy.
e. Or, six balls [palle] in an orle, of which the five lower are gules, but the sixth [the one in chief] is azure charged with three Fleurs-de-lys for Tuscany.
f. Sable a lion or, for Brabant.
g. Argent an eagle displayed gules for Tyrol.
h. Argent a lion sable, for Flanders.
i. Bendy or and azure with a bordure gules for the Free County of Burgundy.
j. Azure, semee of Fleurs-de-lys or, for Artois.

3. The small shields in the corners of the standard bearing a castle on a mount vert, are the arms of the city of Montevideo, which are now reproduced in the second quarter of the shield of the modern Republic of Uruguay.