F for uncle's father is 1/64
For children, the chances to be autozygous for uncle's mother's alelleles is
2 x (1/2)^5 = 1/16
If uncle's father is not autozygous (probability of this is 1-1/64) then
the chances for children to be autozygous for uncle's father's alelleles is also
2 x (1/2)^5 = 1/16
If uncle's father is autozygous (probability of this is 1/64) then
the chances for children to be autozygous for uncle's father's alelleles is also
(1/2)^3 = 1/8
Thus the total coefficient of inbreeding is
F = 1/16 + (1-1/64) * 1/16 + 1/64 * 1/8 = (2 * 64 + 2 - 1)/(16 * 64) = 129/1024 = 0.123

Alternatively:
F = 1/8 * (1 + 1/64 * 1/2) = (128 + 1)/(8*128) = 129/1024
(1/2 appears because half of ancestors were inbred)