In 1901 we already know where Sarah is (from the original question).
Here are some of the other family members.
Leeds RG13/4227 Folio 100 Page 8
Elizabeth Flynn Widow 50 General Servant Domestic Sheffield Yorkshire
Mary Ann do Single 17 Leeds Yorkshire (Deaf and dumb from birth)
are both inmates in the Leeds Union Workhouse.
Leeds RG13/4239 Folio 133 Page 13
Selina Flynn aged 16 and single from Leeds is a Domestic Servant in the household of a Harriet Stephenson at 22 Woodbine Place, Leeds
Leeds RG13/4229 Folio 65 Page 17
Ernest Flynn aged 12 and single from Leeds is a Boarder at Elwood House, Leeds (St Vincent’s House for Boys).
Leeds RG13/4227 Folio 83 Page 9
John Flynn aged 24 and married from Nottingham is a patient in the Leeds Union Infirmary. He is described as a Barman Public House.
I cannot see Walter at the moment.
DS