I had a hard time figuring out what the list of republic flashpoints were with the hard mode option so I tried searching forums and had no luck so went to my trusty Google search and found this list:

REPUBLIC HM FPs:

• The Esseles
  
• Taral V (must complete mission Jedi Prisoner)
  
• Maelstrom Prison (must complete mission Jedi Prisoner and Taral V normal mode)
  
• Directive 7
  
• The Battle of Ilum
  
• The False Emperor
  
• Kaon Under Siege
  

When you finally reach Lv50 you can pick up two quests on the fleet (daily/weekly) that lists all of the HM FPs as well. There is also a sticky on this forum detailing what instance contains which loot.