Malcolm Fleming of Biggar was the son of Patrick Fleming of Biggar the 2nd son of Robert Fleming of Lenzie. His mother was Joan, younger daughter and coheiress of Sir Simon Fraser of Olivercastle, Sheriff of Peeblesshire, for whom the family thereafter quartered the Fraser arms Azure three fraises Argent.

"Sir Patrick Fleming of Biggar, second son of Robert Fleming of Cumbernauld. He is stated to have married one of the two daughters and coheiresses of Sir Simon Fraser of Oliver Castle in Peeblesshire, Sheriff of that county, who was executed by Edward I. On account of this alliance the family thereafter quartered Fraser on their arms. He was father of Sir Malcolm Fleming"

Source: "The Scots Peerage" (1904) Vol 8, page 524. < Archive.Org > citing 8. Caledonia, ii. 922

References

1. "The Scots Peerage" (1904) Vol 8, page 524. < Archive.Org > citing 8. Caledonia, ii. 922
2. The barony of Biggar: from where the Flemings ruled (dead link)
3. Burkes Extinct Peerages 1883 (Fleming of Wigtown)
4. Paul, James Balfour. The Scots Peerage : Founded On Wood's Ed. Of Sir Robert Douglas's Peerage Of Scotland; Containing An Historical And Genealogical Account Of The Nobility Of That Kingdom. Vol VII. "Frasers of Philorth, Lord Saltoun." Begins on page 417. Daughters of Simon Fraser are found on pg 422. < Archive.Org > In 1306 he [Simon Fraser] joined the force of Robert de Bruce, and on 19 June distinguished himself at the battle of Methven.10 He was taken prisoner, conveyed to London, and beheaded with great cruelty. He left two daughters, possibly Margaret and Joanna, who forfeited ten merks of Aldynstone in 1337,11 married respectively to Hay of Locherwart and Fleming of Wigtoun.12
   1. 10 Prynne, 1123.
   2. 11 Cal. Docs. Scot., iii. 388.
   3. 12 Frasers of Philorth, ii. 90 ; i. 13
5. Douglas, Robert, Esq. (1764) The peerage of Scotland: containing an historical and genealogical account of the nobility of that kingdom, ... collected from the public records, and ancient chartularies of this nation, ... Illustrated with copper-plates. < link >
6. < clanmacfarlanegenealogy.info/genealogy >
7. Stirnet Genealogy, Peter Barns-Graham < Fleming01 >
8. Stirnet Genealogy, Peter Barns-Graham < Fraser01 >
9. "Clan Fleming Scottish Society" (2023) < link > Patrick Fleming of Biggar (ca 1270 - ?). Patrick Fleming of Biggar was the younger son of Robert Fleming and his wife, Marjory of Biggar. As second son, Patrick received as his patrimony the lands of Biggar that had come into the family in right of his mother. He married Joan Fraser, an heiress to Sir Simon Fraser of Oliver Castle in Peebleshire. ... His son Malcolm Fleming inherited Biggar and Olivercastle on Patrick's death along with his quartered arms.
10. "Tweedsmuir Parish History: Frasers of Oliver Castle" (2020) < link > Sir Simon left two daughter heiresses. Joan who married Patrick Fleming whose descendants are Lord Fleming and the Earls of Wigton. Mary who married Gilbert Hay whose descendants are the Hays of Yester, the Marquis of Tweeddale. The Barony of Oliver lands were divided between the Flemings and Hays – the precise territorial boundaries are not recorded but the Neidpath site went to the Hays. ...