Fleming Y project at Family Tree DNA
https://www.familytreedna.com/public/fleming/ and others now uploaded to www.ysearch.org
Recommend males have the 37 OR 67 Y marker test at Family Tree DNA and then upload results to Ysearch for more comparisons.
Also females can have the MT test and any can have the newest Family Finder test at FTDNA or the A test at Ancestry and then upload your raw data files to GEDMATCH
If you already have Y dna results they can be uploaded to Ysearch for free. www.ysearch.org
If you live outside USA order your kit from FTDNA (Family Tree DNA) and then upload your Y marker results for the Fleming male who reps for your family.
There are also Cameron, Griffith and other surname projects at FTDNA and they do send kits outside of USA where as Ancestry do not. A simple cheek swab.