Hi SiCallear
I have a lot of Fynney/Finney ancestors, and have tried before to find the will of Fielding Best Fynney. He was a prominent man, and there is lots about him on the www.
I have been unable to find his will though. He is not one of my direct ancestors, so having tried all avenues on-line, I didn't go any further (too much else to do!).
I have looked at National Archives site but it doesn't appear there, or at Borthwick Institute (York).
The other main place is Lichfield Record Office, but their on-line wills index only goes up to 1760.
My next avenues, (if I ever have spare time and not doing my own research!), was (a) to ring Lichfield RO, who will have a look for you to see if it's there, and (b) ring Nottinghamshire Record Office to ask them if it's there.
As I said, there is a lot of information about him on the www, but nobody seems to have found his will.
From a tree I have seen, he seems to have had 5 children - Augusta born 1777, died aged 5, and Samuel Best Fynney born 1779, died 1819, married 1804 Leek. Alfred Augutus born 1782 died 1818, Aldred Caesar born 1786 died 1788, and George Adolphus born 1788, died 1809. (The 'tree' I have is a bit difficult to follow, so there may be more!).
There is a large brass memorial to Fielding Best Fynney in Cheddleton church - this is Staffordshire, although he is supposed to have died in Nottinghamshire, hence the need to widen the search for his will. The border is pretty close there.
THere are many Finney/Finney families around that area, and much published information about them way back - pretty much all stemming from a William Fynney/Fynes who moved to Staffordshire from Herstmonceaux Sussex in the 1500s it appears.
Good luck!