Shinnickburn was named after the Shinnicks. Not sure of the "burn" part has anything to do with a fire but I guess it could. The Shinnicks were most likely from Co. Cork, Ireland. I started a family tree for them last night here on Ancestry.com. At some point around 1860-1870 most of them either died or left the area. Perhaps the women married into other families but the records are hard to search on this website primarily due to miss-recording of thier name and hard to read parish records. Does anyone know where they all went to? David Shinnick seems to have stayed untill around 1900 with his family. Then most of them went to Houlton, Maine.
I also made a family tree for the Mahony family from Cains River/ Blackville, NB. It gets a little hard to follow as there was another family of Mahonys living in Blackville who may have been related but I can't tell. Perhaps some locals would know of a link as it probably goes back to Ireland.