This is the current shared world record:
http://www.fai.org/fai-record-file/?recordId=17704 and
http://www.fai.org/fai-record-file/?recordId=17706

514 km.

Here are the tracks of the latest flights:

http://www.wherearethepilots.com/php/ShowPilots.php?CC=zero&ShowAll

564 kilometers for the three paraglider pilots. 350 miles.

https://www.facebook.com/samuelnascimentoparapente/videos/vb.100002558540996/1110687465693194/?type=2&theater

Andre Wolf and Glauco Pinto flying hang gliders went 612 km, equal to 380
miles. New South American hang gliding records.

Thanks to Raul Guerra and Erick Vils.