Hi
I found William Baillie who died in 1724 on the profile page of my dna match who as the Gipsy ancestry from the South, William Baillie known as the Captain was stated as being from Scotland so there now is the connection you was looking for, this below is the writings in a book that contains many reference's to the Baillies and how the name is spelt several ways, just read the whole book or just go to the back and in the index it shows you the page numbers that you can just read that refers to the Baillies, so use this if you do not like the thought of reading the whole book.
Scottish Gypsies under the Stewarts
by
MacRitchie, David, 1851-1925
Page 111-112
The acknowledged leader of the Baillie tribe in the latter part of the seventeenth century, and until his death in 1724, was the celebrated " Captain William Baillie."
https://archive.org/details/scottishgypsies00macrgoog/page/n122/mode/2upMy dna match Deniece as a Grandmother named lemataney Matthews Mitcham, Surrey, England
1910–1996 r.i.p who's Mother was Lemataney Smith Mitcham, Surrey, England
1887–1969 who's Mother was Lemataney Gardner Carshalton, Surrey, England
1864–1948 and if you go down the Mathews line they wed to Cinnamentia Sinamentey Limmenta (Senna) Cinderella Cooper Epsom, Surrey, England
1865–1943
Also Deniece writes under the title Family tree these names below on the world map of her ancestors,
Agnes Baillie
1803–1879
Borthwick, Midlothian, Scotland
John Baillie
1769–
Borthwick, Midlothian, , Scotland
Captain William Baillie
1661–1724
Hardingtoun Robertoun, Clackmannan, Scotland
John Baillie
1730–1790
Canonbie, Dumfriesshire, Scotland
Mathew Baillie
1694–
Midlothian, Scotland
Matthew Baillie
1710–1816
Midlothian, Scotland
I only can see the first few lines of the Family tree above so do not know how the Baillies connect, Deniece states through her writings that they are all in her Family tree, how this comes to be i do not know, so Gipsy's from Scotland and Gipsy's from England could be in some way in the one Family tree, there is much more information in Deniece profile, I have just kept this short to focus on what you were looking for, Surrey is near to Kent and I am sure many of the other names on this tree will connect to all the Gipsy Family's of the South, just to had I share two dna matches with the Lady named Deniece, one looks to be a Bailey Wharton from America if I am reading things right, they then go on through there own names to rematch to me a great many of the well known Gipsy names that I have spoke of before including another male Bailey that i match to, again from America, I hope I have read things right and I have tried here to put things down in a right true manner, it does look to me that these Baillies from Scotland are in the same Family tree that contain many of the English Gipsy names above, this is what I am reading through a stated dna match to me, i have tried to transcribe everything in a true manner, I hope this information may be of help to you, i do not know if the Baillies from the book are the same as the Baillie's in the Family tree of my dna match above but it looks hopfull through the name of the "Captain William Baillie" and the year of his death 1724, the Family tree and the book share this information its up to you to read into such things and decide for yourself.
michael