The Primera Division club are looking to surpass rivals Rosario Central, who hold the current record with their own 4,350m-long effort.
More than 15,000 fans turned out to unfurl the flag from the site of their old ground down to their current home, the Estadio Monumental in the city of Buenos Aires.
After the demonstration, the flag, which is the equivalent of 316 double-decker London buses lined up side by side, will be cut up and exhibited in various places; including a museum, government buildings and different sporting locations associated with the River institution.
After a slow start to life back in the top division following their 2011 relegation, the Buenos Aires club have hit form just in recent weeks - scoring nine goals and conceding none in their last two games, including Sunday's 5-0 rout of Godoy Cruz.
The longest flag in the world belongs to the Rotary Club International in India, and measures 50,000m.