The Aberdeen South and North Kincardine seat at Holyrood is currently held by the SNP’s Audrey Nicoll.
Flynn said he had sought a dual mandate “for the right reasons” but it did not change the fact he had got it wrong.
He said: “Hands up, I’ve got this one wrong and won’t be pursuing a dual mandate.
“My aim to save the public purse from unnecessary strain by potentially overlapping the role of an MP and an MSP for a short period until the next General Election was genuine in its intent – but doing it for the right reasons doesn’t change the fact that I got it wrong.
“My motivation and central belief remains that Holyrood, as the heart of Scottish democracy, is the democratic platform that will drive the route to an independent Scotland. All of us in the independence movement share that common cause and want to be part of that story.
“Alongside all SNP members, I now look forward to assessing the new candidate selection rules that my party will put in place.”
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Ahead of the 2021 election, the SNP changed internal rules to require MPs to resign their seat at Westminster to fight for selection to Holyrood.
The party’s ruling body – the National Executive Committee (NEC) – could decide to scrap the rule for contests ahead of 2026.
First Minister John Swinney said last week that the SNP had yet to make a decision on whether its politicians could hold a dual mandate – where a single person sits in both Westminster and Holyrood.
Swinney, who held seats at both Westminster and Holyrood between 1999 and 2001, told BBC Scotland News: “We’ve had times in the past when we’ve had dual mandates – I had a dual mandate myself for two years in the early days of devolution.
“The party has got to come to its conclusions about these particular issues and it will do in the fullness of time.”
