Both players will play in the Qatari Stars League with centre-back Flores linking up with former Swansea manager Michael Laudrup at champions Lekhwiya and midfielder Hernandez joining Al-Arabi.
Both transfers are subject to international clearance but the moves will end two-year spells for the Spaniards at the Liberty Stadium.
Chico, 25, made 75 appearances for Swansea after signing from Italian club Genoa and helped the club to Capital One Cup trophy success in 2013.
"It feels like I am leaving my family," Chico said.
"I have really enjoyed my time here
When we won the cup it was one of the best moments in my career."
Hernandez, 29, was signed for a club record £5.55million from Valencia in August 2012.
He made 57 appearances for Swansea but his time in South Wales was often interrupted by injury.
Swansea hope to fill the loss of Chico by signing Federico Fernandez from Napoli and they are currently holding talks over personal terms with the Argentina centre-half having agreed a fee understood to be over £7m.
Source : PA
Source: PA