George FLANNER arrived 27 July 1831 to Sydney. He was aged 18, and was of the
Roman Catholic religion. He was not married. His native place was Essex, England and he was a shoemaker. He had been tried in London, for stealing a musical box. This trial was 6 January 1831. He had no previous convictions, and his sentence was 7 years transportation. He was 5 ft 3 inches, ruddy, fair complexion, hazel grey eyes, light brown hair. He received a ToL in 1836 (36/1783) and allowed to remain in the District of Invermein. The ToL confirms he arrived on the Georgiana in 1831. He received his Certificate of Freedom 17 March 1838. (CF 38/0198, ToL 361783)
http://www.records.nsw.gov.au/state-archives/indexes-online/indexes-to-convict-records/indexes-to-convict-records
On William's marriage certificate it has a note written up the side saying he "did not remember his mother's maiden name", hence the name Jane X, which would support the fact she had already died.
I would assume his father George would have known his wife's maiden name and would have informed them if he was present at the wedding.
There is also a death record for a George Flanner (assuming it is the same as convict records) who died in Victoria 1891 at the age of 80.
Their religion was Church of England but I'm not sure where I should be looking for a baptism record for William (or if one would still exist from 1851/1852).
Church of England baptisms .... in New South Wales you can usually locate a reliable transcription of these records via the free to search online index at familysearch.org You can also actually view the early church records on film held at various public libraries and at NSW State Records Office and at NSW State Library and at family history centres too. C of E baptismal records should be extant. They were recorded in at least two different registers. You need to remember though that Church registers are not public records.
To save you going back over the various Resources Boards at RChat, here's a live link to familysearch.
https://familysearch.org/ Go to their search option, and then to Research by location, and then select Australia. Hopefully you will be at the following link
https://familysearch.org/search/collection/1770729I am not familiar with the administrative practices for the mid 19th Century Roman Catholic denomination in NSW or Victoria, so I hesitate to offer any advice.
Re the information that you read on marriage registrations. I can assure you that in respect of C of E marriages, and likely for all other denominations, the clergy interview the prospective couple in the weeks prior to the marriage. The information is not gleaned on the day of the marriage, and therefore you cannot determine who were the members of the congregation who attended the ceremony, except to note that the official witnesses attended. So, William would have been asked for his mum's details by the clergyman prior at an interview held prior to the day of the marriage. The clergy has then recorded in the margin that the groom "did not remember his mother's maiden name".
I am not seeing how you are determining that the George on the Georgiana in 1831 is William's dad.... I just cannot join those dots.....
Cheers, JM