I'm not sure if this helps or not, as I have not had time to read it myself, but it cropped up in a discussion on British manuals for "skirmishing" type troops, so you never know:-
Britain, G., & Army. (1803). Regulations for the exercise of riflemen and light infantry, and instruction for their conduct in the field.
https://books.google.pt/books?id=QZ8ZAAAAYAAJHaving now had a chance to "speed-read" it, I would suggest the most relevant part is Chapter V from page 26 onwards, which details how a company of riflemen should head an advance guard. Now whilst this is NOT the same as how they would perform on the battlefield, it is IMO indicative - namely the company forms four half-platoons, which would presuably be commanded by officers and senior sergeants, and operates in these sub-units. In a typical brigade skirmish line, there would be a company of riflemen and probably at least three companies of light infantry; I would suggest that one half-platoon would marry up with/support each company, with the fourth half-platoon in reserve under the company commander to provide a close order reserve on which to rally (see previous sections of the book). As others have said, this is not "chapter and verse" on how a detached company of riflemen integrated into the brigade skirmish screen, but it is strongly indicative of how they would
probably have done so.
Hope that helps.