OK - here goes, let's see what proof there is to back up the the account in The Story of Capt John Fleming RN OR the family history compiled 100 years ago.
Unless otherwise stated, the marriages, births and baptisms are in Campbeltown. A huge problem is that many of the records for the Lowland Congregation in C/T prior to 1774 are illegible.
From The Story of Capt John Fleming RN:
...the story begins in 1658 when Fleming’s great-great-great-grandparents, James Flemying and Jenat Strang, from Kirktoune of Kilbryde, now better known as East Kilbride, came to the holding of ‘Bellirgiemore’ in Kintyre.
The OPRs for C/T have the following marriage in 1686 - John Fleming married Jean Strang.
However, I can't find any baptisms for children of this couple.
I can't decide whether this proves that the ancestors of John Fleming RN came from Ayshire or not, but it proves that there was an early Fleming-Strang marriage in Campbeltown.
There are two other male Fleming marriages from the 17th century:
1681 David married Katrine Wallace
1698 John married ????
Next I looked at the info you provided that says John Fleming married 1) Jean Kirkland and 2) Agnes Langwell. I identified the following three baptisms for children of John and Jean, which fits in with the marriage date of 1736 which you provided.
Matthew 12 Nov 1740 John and Jean Kirkland
Matthew 21 Nov 1742 John and Jean Kirkland
Jean 29 May 1745 John and Jean Kirkland
This confirms your account that Matthew Fleming's parents were John and Jean Kirkland. I haven't found a baptism for William, though. However, a William Fleming married Elizabeth Ferguson in Killean parish in 1784.
I can find two baptisms for chidren of John and Agnes Fleming. However, there is nothing to indicate that this Agnes was a Langwill. All the other baptisms from this peiord mention the mother's maiden surname. So whoever this John is, he seems to have married a cousin.
Archibald 8 Aug 1744 John and Agnes Fleming
Janet 14 Sept 1746 John and Agnes Fleming
I also found this baptism.
Elibath b 7 June 1763 John and Ann Langwill
There are also children being born to a James Fleming and Janet Langwill around the same time.
James Dec 1740 James and Janet Languill
Agnus b 29 Oct 1762 James and Janet Langwill
Mary b 9 Oct 1765 James and Janet Langwill
Turning to Matthew Fleming and Jean Porter. I have found just one birth for this couple.
Jean b 15 Dec 1770 Matthew and Jean Porter
I'll leave it at that for the moment and post some other info in the next few days.
Cheers,
Shona