If Savitar is Barry then he probably hails from a very different future, one where Flashpoint never happened and he became a villain as a result.

There are a number of suspects for who Savitar could be but for me personally, I was convinced he was Wally West because Savitar’s metallic appearance reminded me of Daniel West from the comics, and Wally is Iris’ brother in the series. However after the previous episode I’m now convinced that Savitar is actually a future Barry Allen and they are adapting material from the Out of Time storyline, though with their own twists. Savitar has displayed extensively intimate knowledge about every member of Team Flash that only Barry would know and we know Barry is going to meet the younger Savitar who he’ll imprison in the Speed Force soon. He also claims that he is his greatest enemy and while obviously that title belongs to Reverse-Flash and Zoom is still quite frankly his physically strongest enemy, but who is a real hero’s own worst enemy? Themselves! If so Savitar could literally by the physical embodiment of Barry's demons as this isn't a doppelganger who lived a different life from the start, it's the same Earth-1 Barry whose life could have taken an entirely different direction based on a few different choices, which could very cause Barry to question his own capacity to do bad if he sees that one different choice led to him becoming a villain.

The Rival vs The Flash

What if Flashpoint, what is considered to be Barry's greatest failure, actually turns out to be his biggest success because it prevented him from becoming Savitar?

I think there was a timeline where Barry never created Flashpoint and didn’t get the same closure as Post-Flashpoint Barry did from living with his parents, so he became cynical and embittered towards his life, and became much more aggressive towards his enemies and probably became a disgraced hero. Because of that his relationship with Iris probaby failed due to his depression and anger. Caitlin probably still became Killer Frost and while Cisco probably did still become Vibe but Wally never became Kid Flash. However the events of Season 1 and Season 2 probably still played out the same way. "Savitar-Barry" then would have suffered endless tragedies which probably including Iris dying so Savitar-Barry chose to go back and fix events in his life. Of course Savitar-Barry would have encountered his younger self, "Flash-Barry", trying to stop him and interacting with him altered Flash-Barry’s future altering the time Savitar-Barry hails from.

Savitar kills Iris

I think this version of Savitar is his younger self, who hasn't yet been imprisoned in the Speed Force. Also if he is Barry of an alternate timeline, then he's probably fine with killing Iris because she isn't the version he knew.

I think somehow, no doubt a side-effect of the Speed Force and time remnants, that Savitar-Barry actually did succeed in altering the past, but returned to his time to find Flash-Barry co-existing alongside him living a happy life with his friends and family, the life Savitar-Barry sought for himself. As a result Savitar-Barry was now time remnant who can no longer obtain the life he wants, as any alterations he makes will simply benefit his younger self and not him. To make matters worse Flash-Barry is still tied to him as he is his younger self so Savitar-Barry couldn’t just kill him and take his place, and he grew to resent his younger self and sought to ruin his life. Then he ventured back and somehow acquired the Philosopher’s stone and became Savitar. I think the stone somehow empowered him enough to severe the link Savitar had to Barry, “Now finally I am free of you!” as he declares. To ensure Barry lives the absolute misery he lived Savitar kills Iris right in front of him, drastically altering the younger Barry's future. He also saw one suffer a fate worse than death (Wally) and one betray the team (Caitlin).

Savitar vs Barry and Jay

Since Jay Garrick knows of Savitar, as he is considered a legend in the Multiverse, Savitar has been travelling through the Multiverse with his limited abilities to train himself into becoming fast enough to beat his own younger self.

Then later Flash and Savitar have another encounter which ends with Barry opening a portal into the Speed Force and forcing Savitar into it, trapping him countless centuries and driving him completely insane. Driven by revenge Savitar found the means to escape after learning of Flashpoint and Wally West / Kid Flash, but knew from experience that he wasn’t fast enough to stop Barry from imprisoning him and needed to become faster. Manipulating what little control he had over the Speed Force, Savitar began reaching out to other Earths in the Multiverse in order to challenge their best speedsters. Possessing specific individuals and adopting the name Doctor Alchemy, he sought out the other parallel Earth versions of the Philosopher’s stone to grant people powers to form his cult. After sending meta-humans after the speedsters to test them Savitar himself would appear and fight them to increase his own speed, and eventually kill the speedster before moving on. As a result Savitar became a feared legend not just throughout the Multiverse but within the respective timelines of each Earth, as Savitar would challenge more than one speedster from every era of the Earths he visited. As a result of venturing back centuries within the timelines of these respective Earths Savitar was wrongly believed to be the first speedster in the Multiverse. 

Kid Flash

Reason Savitar chose to attack Barry in the past precisely because he needed Wally to be Kid Flash, which is why he hasn't just killed Barry yet because Savitar needs his own younger self's history to play out first.

Eventually he became strong enough to beat Barry and manipulated Julian Albert in 2012 to become the next Alchemy. The reason why Savitar chose to target an earlier version of Barry was because he needed Wally to free himself, and had to wait until Barry created Flashpoint and from the moment he returned from that deleted timeline Savitar began rallying his followers. However as he chose to venture further into the past of Earth-1 there were limitations to what Savitar could do without endangering the existence of his younger self, hence why he hasn’t simply killed Barry yet. I think after Barry confronts the youngest version of Savitar there will be nothing holding him back and he will try to kill Barry and like he did before at some future point, destroy Central City. Of course Savitar will fail and Barry will beat him no doubt in another round of Barry gets faster. 

Savitar posesses Julian

Savitar displays knowledge of events only the original Team Flash members would know, which doesn't include Wally or HR.

Savitar continually says whenever Barry asks who he is that he is “The Future, Flash” but what if he means he is the literal future Flash, as in future Barry. Throughout the season Barry is always being told by people in regards to his timeline changes that he isn’t a god and Savitar is convinced that he is. He also knows key information that he shouldn’t such as Reverb’s existence not to mention he already knows everything about the team, and claims that only he or Barry could live and claims he’s been with Barry since the beginning. He also speaks as though so familiar with Barry even thought he knows he's speaking to the younger Barry who hasn't met him yet. Also some of Savitar’s expressions when speaking through Julian kinda remind me of Barry’s. Again I’ve probably put way too much thought into this but if Savitar is future Barry as I believe he is this is the only way I can make sense of it, keeping everything else told about Savitar in account also.