Did Eobard Thawne intend to replace his rival and become The Flash when he traveled back in time to Barry Allen's childhood? There is reason to believe this was the case, considering the equipment Thawne just happened to have on hand when he was stranded in the year 2000, and the character's goals in the comics.
Of all the enemies Barry Allen has faced as The Flash, Eobard Thawne is undoubtedly his greatest nemesis. Thawne's hatred for Allen became the stuff of legends, with Thawne's efforts to make his sworn enemy's life miserable transforming him into an agent of chaos. Despite being erased from existence twice, Thawne somehow found a way to defy the laws of physics, returning again and again to plague The Flash and his allies, including the Legends of Tomorrow.
The cruel irony of Thawne's existence is that he cannot free himself from Barry Allen's influence on his life without losing the power of a speedster that has come to define him. Like a vampire, Thawne is seemingly helpless to stop and do anything but prolong his cursed existence, despite all the power he possesses. Yet Thawne may have tried to end the vicious cycle through the only means possible that would allow him to remain a speedster and destroy his archenemy, ironically by becoming the very man he hated.
Eobard Thawne's Comic Book Backstory
The Reverse-Flash first appeared in The Flash #139. Originally Eobard Thawne was a career criminal in the 25th century, who stumbled across a time capsule containing a copy of The Flash's costume and (for some reason) a tachyon device that enabled Thawne to give himself super-speed by amplifying the residual energy within the costume. Armed with this, Thawne went back in time to become a supervillain, where he was easily beaten by the The Flash, who destroyed the costume. This made Thawne obsessed with reclaiming the power he'd lost and replacing Barry Allen, taking over his seemingly perfect life.
The 1993 story "The Return of Barry Allen" altered this slightly, changing Eobard Thawne from a career criminal into a 25th century scientist and superhero fanboy. A history buff whose expertise was the 20th Century Age of Heroes and The Flash, Thawne was so obsessed with his favorite superhero that he had plastic surgery to look like Barry Allen, whose identity had long since been revealed to the world at large. Thawne also replicated the accident that gave Barry Allen his powers and tracked down the original Cosmic Treadmill - the device that allowed The Flash to travel through time.
Using the Cosmic Treadmill, Thawne went back in time hoping to meet his idol and win his blessing to officially continue his legacy in the future. Unfortunately, Thawne manifested in the Flash Museum far later than he intended and stumbled across a display regarding The Flash's greatest enemy, The Reverse-Flash, whose true identity had been lost to the historians of the future. To Thawne's horror, the display identified The Reverse-Flash as a madman from the future named Eobard Thawne. The idea that he was destined to become his idol's archenemy snapped Thawne's mind, transforming him into a lunatic obsessed with ruining Barry Allen's life in the same way he now felt The Flash had ruined his life.
Thawne's greatest crime came in the 2009 miniseries The Flash: Rebirth. This storyline revamped Barry Allen's background, giving him a tragic backstory where his mother was mysteriously murdered when he was a child and his father framed for the crime. This was ultimately revealed to be the work of Eobard Thawne, who had traveled back in time and altered Barry's past to make him as miserable as possible while still maintaining the timeline that led to him becoming the Reverse-Flash.
Eobard Thawne's Arrowverse Backstory
For all of the status Eobard Thawne holds as Barry Allen's worst enemy in The Flash and his prominent role in the Arrowverse at large, we know surprisingly little about his background and motivations. He was born in the year 2151 and was obsessed with The Flash and being like him. This led Thawne to replicate the accident that gave Barry Allen his powers and, later, create an artificial Negative Speed Force that he could utilize without The Flash being able to detect him through the Speed Force.
Like his comic-book counterpart, Thawne was once The Flash's biggest fan and he sought to gain super-speed powers to emulate his favorite hero. Thawne revealed this to Barry in the season 2 episode "The Reverse-Flash Returns," stating that he learned his fate was to become The Flash's greatest enemy on his first trip back in time. Realizing that he was never going to be the hero he dreamed of, Thawne decided to become the reverse of everything Barry Allen had been.
As in The Flash: Rebirth, the Arrowverse Thawne apparently went back in time to the year 2000 and altered Barry's past, killing his mother and framing his father for the crime. He later claimed that his original plan had been to murder Barry before he became The Flash, thus preventing himself from ever becoming the Reverse-Flash. The forces of paradox kicked in far faster than Thawne anticipated, however, and he was left powerless and trapped in the past without a Flash to inspire his younger self to become a speedster. This forced Thawne to empower and mentor his archenemy, by killing and replacing STAR Labs founder Harrison Wells and stepping up the timetable of the accident that would give Barry Allen super-speed.
Theory: Thawne Went Back In Time Intending To Become Barry Allen
Thinking on it, it seems improbable that a genius like Eobard Thawne would go back in time plotting to kill his archenemy without accounting for something as relatively simple as the Grandfather Paradox; a hypothetical real-world problem used by physicists to explain why time travel couldn't be used to change the past directly. By killing your grandfather in the past, you would never be born and thus never go on to kill your grandfather. (Fittingly, the Grandfather Paradox was utilized to defeat the Reverse-Flash in The Flash season 1 finale, with Eobard Thawne being erased from existence after his ancestor, Eddie Thawne, committed suicide to prevent him from ever being born.)
Another improbable aspect of Thawne's plan to kill a young Barry Allen lies in the technology he had on hand when he became trapped in the past. A series of flashbacks in the season 1 episode "Tricksters" revealed that Thawne transformed himself into a perfect clone of Harrison Wells by utilizing a piece of future technology which overwrote his DNA, effectively changing Thawne into Harrison Wells on a genetic level. The device also gave Thawne Wells' memories, allowing him to flawlessly impersonate Wells and take his place in the past. It seems unlikely Thawne would just happen to be carrying something like this when he traveled to the past or that such an item would be widely available, even in the 22nd century.
Thankfully, the only evidence we have of Thawne's intentions in traveling back to the year 2000 are his own words. Given that Thawne is a gifted liar and the fact that he orchestrated far more complex plans involving time travel before, we can safely presume that he never truly thought he'd be capable of killing Barry Allen as a child and not have it result in him losing his powers. This begs the question; what was Thawne's true goal?
The answer is simplicity itself when one considers the likelihood of Thawne just happening to have a device capable of transforming himself into someone else by copying their DNA when he went to the past; Thawne intended to become a young Barry Allen. This would explain all the evidence on hand and why Thawne seemingly overlooked the paradox implicit in trying to kill his archenemy. It would also further emulate Thawne's background in the comics, where he dreamed of someday becoming The Flash.