The SNP is yet to decide what its rules will be for candidates at the next election.
The change on dual mandates led to then-MP Joanna Cherry pulling out of the selection contest for the Edinburgh Central seat.
Health Secretary Neil Gray also had to resign as an MP before being elected to Holyrood in 2021.
Cherry - who lost her Westminster seat in July’s general election and has ruled out a bid for election to Holyrood in 2026 - said the SNP rule was “person specific”.
Responding to Flynn’s column, she added in a post on X that the rule “served its purpose” and predicted it would not be in place for 2026.
The Scottish government recently said it intended to launch a consultation on proposals to ban MSPs from holding dual mandates, though any changes are not expected to be introduced in time for the 2026 election.
Flynn has been tipped as a future SNP leader, but he predicted there would not be a contest to replace Swinney for “very many years”, adding that he had full confidence in the first minister.
He told the Press and Journal: “Of course I want to do everything I possibly can to help my party and help my country and that will never change.”