Is it possible that I might be related to James I of Scotland in family tree.
As are probably 99% or more of anyone alive with any European ancestry. Going back 15 generations, there just aren't that many people with documented lives that you can trace back to. So if you really can go back that far, you are doing to run into the same people everyone else does.
The real question is, are these links back to him all correct? You need to verify and document with sources each link in that chain. Much before 1700, you propably won't be able to do this yourself, but need to link into a verified, recognized as accurate, source that correctly documents the rest of the line (not wikipedia!)
Welcome to the "Community.FamilySearch" Forum.
I am just another 'lowly' User/Patron ...
Certainly possible; and, 'looks' that way. through "View My Relationship". in "Family Tree", of 'FamilySearch'.
[ ie. Through your "Ancestral" Lines, in "Family Tree", of 'FamilySearch' ... ]
As an aside ...
IF, you have not already; and, you want to 'see' even more interesting "Relationships" that you may have. in "Family Tree", of 'FamilySearch'; THEN, ...
You might want to consider trying/using (BYU) RelativeFinder, which is one of a number of the, Third Party Applications, that are Certified to work with Family Tree of 'FamilySearch'.
BYU = Brigham Young University, in Provo, Utah, USA (ie. the Church University).
Specifically, from the Family History Technology Laboratory, of the Computer Science Department.
Provide, your "Ancestral" Lines, in Family Tree of 'FamilySearch', are somewhat extensive ...
Then, using (BYU) RelativeFinder, you should be able to 'see' one's "Relationship" NOT only with, "Famous People"; and, many, "Others"; but, ALSO between, (1) you and a "Deceased" individual/person (if, there is one of course); and/or (2) two (x2) "Deceased" individuals/person (if, there is one of course); and/or, (3) you and a another "Living" User/Patron (if, there is one of course); PLUS, one can ALSO "Print" the connections/links between them.
(BYU) RelativeFinder digs (pun intended) a lot DEEPER in Family Tree of 'FamilySearch', than 'FamilySearch' does.
To use (BYU) RelativeFinder, it is just a matter of "Signing In", with your 'FamilySearch' credentials (ie. User Name; and, Password); accepting the "Conditions"; and, off you go.
Here is direct link to (BYU) RelativeFinder:
(BYU) RelativeFinder has MANY 'Bells and Whistles', that you might find useful.
Apart from "Famous People" and "Others" ...
(BYU) RelativeFinder has some interesting options ...
There is an option to see if there is a 'Connection' between you and a "Deceased" individual/person in Family Tree of 'FamilySearch'.
There is an option to see if there is a 'Connection' between two (x2) "Deceased" individuals/person in Family Tree of 'FamilySearch'.
There is an option to see if there is a 'Connection' between ("Living" - Users/Patrons) Friends in Family Tree of 'FamilySearch'.
ps: Caveat - Please be aware, that NOT "All" Users/Patrons, may have success; but, hopefully, many will.
I am not so sure that Gordon's comment about 99% is accurate. I heard it said some years ago that approximately 50% of people with British ancestry can trace back to King John who is further back than King James. You need ancestors with money and/or status before you can realistically expect to get back to a king. For many, their ancestors were all of lowly status and they did not inter marry with those of higher status.