I don't know where Flowers Cove is, but have a family of Walshes in Northern Bay, in and around Job's Cove. Some of their births and marriages are listed on the Newfoundland's Grand Bank's Webpage. Look under the listing for Vital Statistics for Corpus Christi listings. Information can also be found under the heading of Church Records. Look in the Church of the Assumption records. You may be able to find some Walshes there.
Hope this helps!