Not sure if this is much help to you.
I've found an Ann Sinclair age 24 with a son David Sinclair age 3, living as stepdaughter to George and Janel Birrell, Baldridge Burn, Dunfermline. George was a Linen Damask Weaver. There was another stepdaughter - Eliza Peterson Aged 17.
This Ann was shown as being born in Edinburgh. I surmise her maiden name was Peterson (but that's only a guess). Her son David was shown as born in dunfermline.
The only John sinclair B 1839 I could find in Fife was married to a lady called Christian , and they lived in Proterhill, Dunfermline Landward.
There is a John Sinclair Age 20 working as a plowman (servant) at Broadleees House, Kinghorn - this was a 100 acre farm run by James Stooks and employing 3 men and 1 boy. This John Sinclair was born in Kinghorn - so I don't think this is yer man.
Obviously I've focused on those living in Dunfermline or nearby.
Sorry if this isn't much help
JULIAN