Here is what I have so far. I am hoping to find some cousins: I am stuck at Robert Kennedy near the bottom of the page.
(All are born, lived and died in Newcastle Upon Tyne unless otherwise noted),

~Grandparents:
William Thomas Flanigan Kennedy
B: 1904
M: 1927 to Margaret Evelyn Ridley (Hexham, England)
Immigrated to Hamilton, Ontario, Canada in 1929
D: 1942 in WW2, in combat Dieppe, France

~GRT-Grandparents:
William Thomas Hamilton Flanigan Kennedy
B; 1879
M: 1901 to Edith Isabel Ayre (Bishop Auckland, Durham, England)
D: 1959

Children:
Herbert Kennedy 1902 – 1965
John Kennedy 1903 –
William Thomas Flanigan Kennedy 1904 – 1942
Sarah Kennedy 1906 –
Robert Kennedy 1918 – 1992

~GRT-GRT-Grandparents:
Archibald Kennedy
B: 1856
M: 1882 to Sarah Maria A Flanigan (Carlisle, Cumberland, England)
D: ? Questions regarding his death date. (1914 or prior to 1901)

Children:
William Thomas Hamilton Flanigan Kennedy 1879 – 1959 (He was born Flanigan, then took on Kennedy name when parents married in 1882)
John Peter Kennedy 1886 –
Joseph B Kennedy 1888 –

~GRT-GRT-GRT-Grandparents:
William Dixon Kennedy
B: 1824
M: 1830 to Ann Young
D: 1871

Children:
Robert KENNEDY 1850 –
Ann KENNEDY 1852 –
Margaret Alma Kennedy 1855 –
Archibald Kennedy 1856 – 1914
John William KENNEDY 1858 –
Andrew KENNEDY 1861 –
William Kennedy 1862 –
Mary Kennedy 1866 –

~GRT-GRT-GRT-GRT-Grandparents:
Robert Kennedy
B: ?
M: 1814 to Harriott Dixon in Kingston Upon Hull, York, England
D: ?

Children:
Maria Kennedy 1816 – (Not sure if she is theirs, but fits the time-frame)
WILLIAM DIXON Kennedy 1824 – 1871

... NO OTHER INFORMATION.

Hoping to find some cousins.
Rhonda Kennedy