I am no longer sure about the Campbeltown connection, but would like to know about your Kilmarnock Adam's!
I have James Adam born 1828 in Inveraray, Argyll. His parents were John Adam and Mary Collins, married the previous year in Inveraray.
James married Jane/Jean Brown in Dundonald, Ayrshire in 1851 and they had the following children - Mary 1852 (Troon) Jane 1855 (Rothesay), John 1857, Ann 1860, Francis 1864, James 1866, William 1869 and Norman 1871.The last six were all born in Kilmarnock. There appears to have been another daughter in the 1850's, but no details yet.
James was a baker and the business appears to have been passed on to my great grandfather, Norman in the 1890's.