Because Florence was born after 1911, if you look at the England & Wales birth index you can find her mother's maiden name.
So Florence E Jones's birth was registered in the January quarter of 1917 (Vol 11B Page 688) and her mother's maiden name was TYLER.
I then looked for their marriage in the marriage index: Robert G Jones married Elizabeth E Tyler in Conway in 1914 Qtr January (Vol 11B Page 583). I know her first name is different from your post, but it may be a case of she was always known as Mary. If you were to get Florence's birth certificate this would show her mother's forenames.
I had a look to see what other Jones births there were with a mother named Tyler, and there is one that I think would be a sister to Florence: Phyliss M Conway 1920. Charles V Jones was born in Conway 1915.
The last census published in the UK is the 1911 census. I did do a search for Robert G Jones living in Conway and there are 3 hits.
To take this further, you really ought to purchase their marriage certificate as that will their ages, occupations, where they were living, their father's names and occupations.
I don't know where you live but even if you are overseas you can purchase a certificate direct from the General Registrars Office at a cost of £9.50. The link that you need is:https://www.gro.gov.uk/gro/content/certificates/Login.asp
Hope this helps you