[4] In 2006, Cordner signed with the Northampton Laurels FC in the WPSL, the highest division of women's professional soccer available in the United States at the time.

"[8] She made four appearances playing a total of 99 minutes and scored one goal helping the Roar ultimately win the 2010–2011 W-League Championship.

[3][9][10][11][12] Cordner played for San Juan Jabloteh FC of the Lucky Bakery Women's Super League in the summer of 2011.

[16][17][18] On 19 June 2013, it was announced that Cordner had signed with the Seattle Reign FC part way through the inaugural season of the National Women's Soccer League.

[19] Of the signing, Reign FC head coach Laura Harvey said, "At every level she has played Kennya has shown she knows how to find the net.

[22] Mid December 2021, Cordner moved to Turkey, and signed a deal with Fenerbahçe from Istanbul to playe in the 2021-22 Super League season.

In July 2011, she scored nine goals during the Women's Olympic Football Qualifying match against Dominica leading the Trinidad and Tobagonian squad to a 15–1 win.