'A Dictionary of English Surnames' has: Gilkin, Gilkins: Gilkinus de Braban 1296 FrY (FrY= Register of the Freemen of the City of York); Richard Gylekyn 1317-18 FFSr (FF=Feet of Fines, Sr=Surrey); Richard Gylkyns 1332 SRWo. (SR=Subsidy Rolls, Wo=Worcestershire);Gill-kin, a diminutive of ON (ON=Old Norse) Gilli. v. Gill. Irish Gill and Galloway MacGill, MacKill are all from Ir, Gael Gille 'servant'
It also says that to add the -kin suffix, was frequently used as personal names, sometimes to distinguish son from father, sometimes as pet names. ie: John=Jankin, William=Wilkin are both used as names of the same man. It was very common to do this in the middle of the thirteenth century and fourteenth century. It is thought that this was brought from the Netherlands. -kin names were common in Cheshire at the end of the thirteenth century.