The competition is set up in the memory of Fletcher, the only person to have been chairman of both the Institute of Practitioners in Advertising and the Advertising Association, and a prolific writer.
The closing date marks the first anniversary of his death last year.
Entries, which will be competing for a £2,000 prize and publication, need to be up to 4000 words and use advertising in the plot somewhere.
The chairman of the judges is the founder of Waterstones, Tim Waterstone, and other supporters include David Abbott, Adrian Vickers, Robin Wight, Lord Smith of Finsbury and Lord Black of Brentwood.
For full details, visit www.thewinstonfletcherprize.co.uk