The surname Fleming, with it's variants Flemon, Flemming, Flemmyng, Flemminge, originally came from Flanders. The Flemings arrived in Ireland at different times and may have descended from different families of the name in Flanders. In the 17th Century Fleming was a principle name in Limerick. In 1659 there were 12 Flemings listed in the Barony of Costlea. This information is from the book "Families of County Limerick Ireland by Michael C. O'Laughlin, president, IGF.
My Flemings came from Ballylanders which is indeed in the Barony of Costlea. Thomas Fleming and Mary Hennessy married in Ballylanders, Co Limerick about 1845. Of their 10 children that survived to adulthood, all emigrated to the United States. One, Patt, returned to Ireland claiming, according to family stories, that one had to work too hard in the United States. Patt Fleming opened to grocery and spirits shop in Dublin on his return to Ireland. Of those who remained in the all settled in the Midwest. Today their descendants range from coast to coast.