Hi,
The short answer to your question is no I don't. I know that two brothers named Henry and Richard Richmond came over to Scotland with my great great grandfather, Charles Walker, and his younger brother John. All I know for certain is that they were born in County Antrim.
The Irish Times tells me that there are 9 parishes in County Antrim where the surnames Walker and Richmond co-existed at the time of Griffiths Valuation. The Richmond boys' father was John Richmond and their mother was Jane Henderson. That narrows it down to Drummaul, Carrickfergus, Kilraghts, and Kirkinriola. That is all I have to go on. The Richmonds had a stronghold in the Rasharkin area and there are Walkers and Richmonds in nearby Craigs Parish. However, there are no Hendersons to be found there.
I had almost given up until the 1901 census came online and I discovered a family of Richmonds in Drummaul with the same first names of the two who came over to Scotland. The name Richard Richmond does not appear to be very common. A coincidence, perhaps, but they shared a common landlord with Walker families and there were also Hendersons in Drummaul.
It might be time to let it rest but it would be nice if I could find out more about them.