Welcome to RootsChat, JasJer.
Was Brannigan Margaret's middle name? If so the connection must be on her side.
If not ....
It's always useful to give a date of birth, even if only approximate, when you're asking about someone. Fortunately Felix is a very unusual name in Scotland so he's not going to be too hard to find.
There are three recorded births of Felix B*r*n*g*n in Scotland
1879, Liberton, Midlothian
1896, Glasgow
1900, Glasgow
and two deaths
1873, Haddington, an infant
1925, Dalziel, aged 49
1956, Glasgow, aged 55
There are three in the 1901 census
Glasgow, aged 4, parents Nicholas, born Ireland, and Margaret
Dalziel, aged 24, born Ireland, mother Ann
Gasgow, 9 months, others in household Annie, Bridget, Henry and James
Nicholes Branigan and Margaret White were married in Holytown in 1893.
So it looks as if your Uncle Felix was born in Glasgow in 1896 to Nicholas Bran(n)igan and Margaret White.
However I don't see any record of a death of Nicholas, Margaret or Felix in Scotland, and there is only one death after 1973 of a B*r*n*g*n with mother's maiden surname Whyte. Did they perhaps return to Ireland, or emigrate somewhere?
There's a birth of a Nicholas Branigan, son of Felix Branigan and Margaret Doran, at ?Maghernahely, District of Mullaglass, Newry, County Antrim, on 5 February 1867, who looks a likely candidate.
But don't assume - check Nicholas' marriage certificate to see that the parents' names match.