The sitter, Colonel Banastre Tarleton (1754 - 1833) distinguished himself in the American War of Independence, and returned to England as a lieutenant-colonel about the beginning of 1782. Later he was Member of Parliament for Liverpool, a general and a baronet.
This work was painted in 1782. Tarleton is in the uniform of a troop, raised during the American campaign, known as the British Legion or (for the cavalry part) Tarleton's Green Horse, of which he was commandant.
It is assumed that the flag above him is of the British Legion. In 1781 Tarleton lost two fingers of his right hand, as Reynolds discreetly shows.
From The National Gallery Podcast: Episode Forty Nine, November 2010