Nope!
Ha, I win.
Rick Flagg Jr.
"I tread the same path my father did, never escaping from his shadow."
Dad was in Suicide Squad, so was Rick.
"The same tragedies, cuts, and loss of hope."
Both Flaggs lost hope towards the end of their lives, losing many comrades and loved ones, and wanting to die.
"No matter how hard I fight the good fight, or who I lead into battle,"
Who I lead into battle was a big one. Flagg Jr lead heroes and villians, not just heroes.
"Will it even matter in the end?"
Rick thought his life was useless towards the end.
"Will you remember me when I'm gone?"
Rick lost everyone close to him with the exception of Nightshade, whom he never realised his romantic relationship with. He was too depressed.
"Just to die and be free,"
Hello? SUCIDE SQUAD! I was sure someone would get that!
"end it all,"
A common euphanism for Sucide.
"here, in fire,"
Flagg died in a nuclear explosion inside of... *drumroll*
"in the giant's lair."
Joutenheim, which means lair, or city of giants.
Hey, its a riddle sucker, I'm not going to make it easy.
The main clue was the death wish, sure others may have daddy issues, but how many of them want to die?