Well Bloody Hell!
I just spent almost an hour composing a very detailed response to your query with links, notes, sources, etc., then lost the whole thing right before I posted it when a storm started here.
So, here's the short version and if you'll PM me with your e-mail address I'll be glad to send you the sources and documentation.
Monmouth's Royal English Regiment (multiple battalions at various times). I would clothe them in gray with blue facings as we have good documentation that they were in that uniform after the Rhineland campaign, specifically in 1679 on parade. For a flag (or flags) I would think something like the flags carried by James Foot Guards at a later period, but with Charles II's cipher.
Douglas Scots were originally formed for service in France, are considered part of the ancestral tree from the Hebron Regiment in the TYW through to the Royal Scots. René Chartrand has depicted their uniform in 1669 as red faced white and there are numerous published versions of Hebron's flags from the TYW and the Eighty Years War against Spain. I would use this uniform and probably update the Hebron flags.
Hamilton's Irish also included the remnants of Roscommon's Irish (Dillon). It's questionable whether they would wear their traditional red at this early date, and could be depicted in gray with colored facings. For flags I would use a variation on Roscommon's flags shown in Mark Allen's WI article in issue 54.
The most reliable OB that we have found is in the Marburg Digital Archive. It is a map done by the premier cartographer and engineer to the French Court of the battle of Enzheim done by an actual witness to the battle, Sebastien Beaulieu de Pontault.
http://www.digam.net/image.php?file=dok ... jpg&b=1200
This map shows 7 total formations, 3 labeled Monmouth, 2 labeled Hamilton, and 1 each for Douglas and Churchill. Two things, Turenne was known to "create" units to fill tactical roles, and the French sources are going to name proprietary Colonels that were "known". I suspect that the 3 attributed to Monmouth are probably the re-organized remnants of his battalion, Skelton's battalion, Vaughan's battalion and Lockhart's battalion. Churchill had already received his French commission by this time (March of 1674), and the battalion attributed to him is probably Lord Peterborough's (who resigned over the affair) mixed with the "volunteer" recruits that he took from the Guards members who were re-called to England. The 2 battalions attributed to Hamilton are probably his own and Roscommon's.
So, there you go Sir, and I would paint them and enjoy them until (or if ever) another reliable source is discovered that contradicts the above.