Her birth; note that only Medway contains Rochester and the use of Harvey as the last forename:

Surname First name(s) District Vol Page
Births Mar 1868   (>99%)
Hamilton Florence Margaret Ripon 9a 77   
Births Mar 1869   (>99%)
Hamilton Florence Harvey Medway 2a 472
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The only Florence H Hamilton marriage in is 1934, far too late for childbearing.
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In the 1891 census there was in Weymouth, Devon a Florence Hamilton with her cousins William A Wetherall, a brewer, and his sister Marianne Wetherall:

First name(s) Last name Relationship Marital status  Gender  Age  Birth year  Occupation  Birth place

William A Wetherall Head Married Male 53  1838  Brewer  Woolwich, Kent
Marianne Wetherall Sister Single Female 60  1831  -  India
Florence Hamilton Cousin Single Female 22  1869  -  Woolwich, Kent
Hannah Brown Servant Single Female 45  1846  Domestic Servant Cook  Waterford
Elizabeth Warne Servant Single Female 25  1866  Domestic Servant Housemaid  Weymouth, Dorset

I have not previously found these Wetheralls.
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In 1901 there was this small family in Cowan Street, Camberwell:

First name(s) Last name Relationship Marital status  Gender  Age  Birth year  Occupation  Birth place

Florence Hamilton Head Married Female 33  1868  Housewife  London, Middlesex
Maud Hamilton Daughter - Female 11  1890  -  London, Middlesex
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No other entries for Florence that are tempting.
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