I'm sorry to say that I don't have any info on the 'descendents' of Lydia Flintham, but I have a tidbit of info that might help in your search...
I have an abstract of a Maryland perogative court record from 1766 indicating that William Flintham had died, his 'next of kin' was 'Lydia Jr' and his administrator was George Bond Jr.(this George is in my family line)
I have the will of George Jr's dad (George Bond Sr.) who died in 1777 naming a 'Mary Lidia Flintham ' as his granddaughter.
The assumption here is that George Bond sr. had a daughter who married a Flintham boy, thus producing the granddaughter Mary Lidia named in his will. The other assumption is that the Flintham boy that married the Bond girl was no longer living when William (his dad ) died and was the only son . That would be why the William from the abstract had no living sons to be his 'next of kin' or administrator. (Thats why William apparently named 'the brother of his sons wife" the administrator)
If this theory is true, then this "Flintham line" effectly ends with Mary Lidia. (If there were no other Flintham boys)