Sorry if it's too long or badly written. I hope it gives you an idea of how I imagine Flint's mind/goals/personality. Just choose whatever's more fun and/or easier to write for you, I won't complain or anything, I trust your judgment and writing capabilities. And if you don't like something or want me to change it or if you want me to give more info about something, just say so.
First of all, if Steve needs help to GTFO of this universe, then Flint would do whatever he could to help, he really likes Steve, since he's one of the few people AIs who were nice to him and talked to him and actually helped save his life multiple times. If there was anything really important that needed doing on the other side, then he'd probably help with that too. Otherwise, he'd probably just make sure Steve had a way to contact him, if he ever needed anything. Preferably a way besides doing Morse code to his brain with the shock implant.
If there's nothing of terrible importance, then Flint would probably try to settle down somewhere. He'd probably go for something like trainer, maybe in police or military, since he always wanted to help others and pass on his knowledge to others and he believes he can put his skills with people to good use. He wouldn't go for anything too important unless it was necessary for him to step up and take responsibility to save others, because despite his big talk he doesn't actually believe he's good enough for something as important as that.
But he'd be restless, couldn't really settle down. He'd probably be pulling harmless pranks on his superiors/recruits or taking his recruits out on (relatively) safe and fun (and probably wacky) adventures whenever opportunity presents itself. And he'd probably be talking about the good old days a lot, the old world and all the things there (movies especially). I guess he'd be kinda like a less senile, more dangerous commandant Lassard.
However, he was always self destructive, a man of extremes. Smart and dumb, brave and a coward, success and failure, happy and depressed. An old man with a tendency to look behind, at his past mistakes (perceived or actual), even as outwardly he tries to appear happy and fun and cool, perhaps sometimes trying too hard.
He believes he's too old and too messed up to find a friend and/or a romantic partner he could really connect with and he believes he doesn't deserve to have such things due to his perceived failures and mistakes he's done, so if he ended up wherever he ends up alone and wasn't lucky enough to find that someone that could slap him in the head, tell him to stop being an idiot and truly enjoy his life, he'd probably keep spiraling downwards and becoming more and more self destructive. In the end, he'd either do something really dumb and end up hurting someone or merely end up wanting to escape. He'd find one conflict or another he could get behind and just go there to fight until he either died or became as good as dead, a dumb killing machine that tries its best not to think about anything else. That's because he believes that he might find peace by embracing the monstrous killer he believes he is. In the end he'd probably end up like a WH40k dreadnaught: a senile driving force that some call a hero entombed in a killing machine that's woken up and pointed at what needs killing, doing its "duty" while spouting propaganda like only a man that has become incapable of truly believing in anything can. After all, he did spend a large part of his life being a tool for propaganda before he met and fell in love with that genemodded girl that changed his views and his life. He could end his life in the same way, being a mindless tool.
On the other hand, if he did find/end up with someone that could help him balance his life and keep it together, he'd probably live a more happy, more peaceful, less self-destructive life. He'd pass on his teachings and try to make the world a better, less violent place, filled with brave, intelligent defenders with cool one liners. When it was time to retire, he'd find someone who he could trust, someone who could be worthy of the legacy of Gilgamesh, and pass the suit on (which at this point I'd imagine it would have so many add-ons and upgrades it would barely resemble the original, judging by how many stuff I've put in that thing so far) and then live out the rest of his days in peace with his family (adopted or otherwise, depending on how things turn out). Unless of course some great calamity demanded his attention, in which case he might return to duty, either in Gilgamesh or as a general or other leader, depending on how old he was and what the nature of the emergency was. Perhaps it is fate that he should die in one last great fight for others.
There's also a middle ground. He finds a challenge. A serial killer, a great criminal mastermind, something that can keep him occupied. A Batman to his Joker, in a way, someone that gives him purpose and a reason to keep it together, because he gives him an enemy and a goal to work towards. But I think the other two might be more fun to write.