A/N: The Eobard reference I don't believe he says to Barry in canon directly from what I recall but I'm assuming he could have done during their little Flashpoint feeding chats.
Actually getting the time loop stuff right when writing Savitar is...tricky. Not sure if this does work as it should but having spent a lot of time on reddit reading up the theories around Savitar's creation and looping existence I think the best answer is don't think about it too much because understanding the bootstrap paradox as it relates to an object with no start point/creation is very different to understanding exactly how it would relate to a character who has consciousness and experiences memories linearly. Some of the weirdness of that and how it would affect perception of the memories he has can probably can be handwaved by Speedforce connection and related Speedforce prison sanity issues too.
Though I'd add that it does seem likely that Savitar has memories from the original 3x19 'The Once and Future Flash' timeline - where supposedly none of them, Barry's time remnant who would become Savitar included, knew who Savitar was (unless all were lying to present!Barry when he visited). That timeline would be branched into a divergent timeline once Barry did that trip to the future and changed his possible future to be different from that one, but there's nothing to say Savitar won't recall that as he experienced it first, as well as getting new memories from Barry as changes are made to his past.
So, er, it's complicated but I hope someone enjoys this twisted little bit on how he got his scars because the show only gave a possible theory on that from Tracy, without confirmation from Savitar.
Iris brings her hand up to touch his face, her hand tracing the scars lightly, barely a hint of sensation felt through the damaged tissue. The absence of feeling her motion brings him reminds him she's as good as the ghost he's thought of her as for so long. Eobard's words echo in his mind 'To me they've been dead for centuries'. Iris is no different to him; his past and future blend together easily, interchangeably thanks to a timeless stint in the Speedforce. All of it is pain to him, all that matters is the desired outcome – his creation, his rise to Godhood, his survival.
He remembers though, the moment he was truly made. Not by the Barry he was, but by another hand that had cupped his face almost tenderly.
There had been some mix of pity and reverence in Killer Frost's eyes in that moment. He'd been brought to his knees in front of her, another icicle in his leg, third time's the charm she'd said. He'd wondered then what she had planned for him because if there was one truth he'd still foolishly held onto it was that Caitlin Snow couldn't kill Barry Allen, no version of him. She'd hurt him countless times, delighted in getting the best of him, but she'd never seriously tried to kill him – until that day. His heart had shattered over and over to see she wasn't remotely his friend anymore as she took down time remnant after time remnant at Savitar's side.
He hadn't been Barry, he'd been just another Barry, another Barry breathing still whilst his other selves lay sprawled about no longer taking breath, massacred. There'd been only two of him remaining, he hadn't known if it would be him who would die or whether they might both fail in their vengeance. The ice had hit his senses in that tiniest fraction of a second he'd hesistated to move away from her, whilst he'd looked into her eyes wishing he had answers for the joy witnessed in them. He'd gone colder than he'd ever known, his body so cold so suddenly, so deeply that he'd felt trapped by it.
For the shortest instant his face had burned in agony before it froze so completely he'd felt nothing where her hand was, except distantly numb at the edges of where the ice kissed his skin. She'd smiled at him, taking her hand away, pleased at her handwork as he gasped for breath, finally able to vibrate again to shake off the cold and get back to functional. He hadn't hesistated again, stabbing her directly in the chest with a power dampening serum tranquiliser provided by Cisco. He'd turned to see his other self blast Savitar into the Speedforce. He'd thought it was over when he'd seen that, he'd thought they'd won but that was the moment their paths diverged, marked only by the frostbite settling into his skin.
End note: It's not clear just how cold Killer Frost can go because the show isn't big on details for mechanisms of her powers but if she can get to near absolute zero for example then probably she could damage his cells significantly enough they might not be able to heal or only heal incredibly slowly. Certainly she was powerful enough to kill The Black Flash at the end of 3x23 so I don't think it's necessarily a stretch here.