I thought this was pretty much it. And yes, I quoted myself.
So, shortly after birth Mrs. Fred dies. Then Fred gives his daughter up for adoption. Being a small town when his unknown daughter is of age they meet and get married. Neither one knows they are related. They play cards with friends and the friends figure out who the daughter is. They discuss telling Fred. Later Fred is arrested and the daughter is in shock.
So is the only thing left how the friends knew?
They saw the blood type and the age of the daughter along with the resemblance to Mrs. Fred. Is that right?
Fred's daughter is born while he is in Vietnam, and with his wife not being in the best of health even then, the daughter is put up for adoption and eventually winds up being raised in Minneapolis. Not long after Fred returns from war, his wife dies. Fred never really moves past his wife's death (the living room is largely unchanged, he drops out of social events with this friends, etc), so when, a number of years after his wife died, he meets someone who in many ways reminds him of his wife, he immediately falls for her, never suspecting she is in fact his long lost daughter.
Because Fred and John were together in Vietnam and in military hospitals afterwards, John (and through him Jane) knows Fred's ultra-rare blood type (AB-, if you're interested). When Jane spotted on the blood donor certificate that Flora was also an AB- and heard Flora comment that she had been born in that same very small town, she knew the odds of two people from the same town having that same blood type were vanishingly small. When Flora mentioned she was adopted, Jane became certain that Flora was in fact Fred's daughter.