Warning: The following contains SPOILERS for The Flash season 7, episode 15, "Enemy At The Gates."
The Flash season 7 episode "Enemy At The Gates" revealed that Barry Allen owns a car, immediately prompting many fans to ask just why Barry Allen would ever own a car. The question was echoed in the episode by Chester P. Runk, who inquired as to the existence of a Flash Mobile after catching Barry Allen walking into STAR Labs with a set of car keys. However, while it is seemingly nonsensical for the self-described Fastest Man Alive to own a car, there is a logical explanation for why he might.
"Enemy At The Gates" found Barry Allen attempting to conduct a pregnancy test in secret on behalf of his wife, Iris-West Allen. Beyond wanting to keep their efforts to conceive a child as a surprise to their family and friends, Barry also had to conduct the test himself in order to hide his secret identity as The Flash. This was due to metahuman DNA signatures causing mispresented hCG levels in standard pregnancy tests without proper calibration. Given that, Barry had to drive the samples he took from Iris to STAR Labs, rather than run there at superspeed as he normally would. This led to a comedy of errors, as Barry's efforts to run the test in secret were continually interrupted by well-meaning friends, who were wondering why he was carrying a bag full of blood and urine samples and why he, of all people, was driving to work.
Logically, there is little reason why The Flash should need to own a car. Even at Flash's lowest speed in The Flash season 1, Barry Allen has always been fast enough to get across town in seconds. Barry also wouldn't need a vehicle to protect his secret identity, as Central City is large enough to have an extensive public transit system and flashbacks from before Barry Allen had superspeed powers showed him using the bus and train to get around town with few problems, apart from his own natural inability to show up anywhere on-time. However, using only superspeed to travel would likely risk Barry's secret identity, so having a vehicle would be a useful way to protect his superhero alias.
The absurdity of The Flash owning a car has been raised in other media. The Justice League animated series episode "Eclipsed" revealed that The Flash had bought himself a custom Flash Mobile, a red van with yellow lightning decals, using the proceeds from his first wave of endorsement contracts for Lightspeed Energy Bars. When a proud Flash showed his new ride off to an incredulous John Stewart, the Green Lantern's first question was "Why do you need a van?" He immediately thought better of it and told The Flash not to answer the question, after noticing the spare-tire cover for the van had the words "Wild Thing" written on it.
While it was amusing for The Flash to play up how pointless it is for Barry Allen to own a car with his powerset, there is a logical explanation for why he would have access to a car. While he can easily run to any point in the world in seconds, his wife, Iris, does not have the same abilities. As such, the car was probably more for her benefit, but traffic being what it is in a major metropols the size of Central City, it was usually better for Iris to take the bus or train to work, which was why the car had never been mentioned until "Enemy At The Gates." Besides that, the are occasions when having a car could be useful for a reporter, who might have to drive outside of Central City for the sake of a story. Given that, it seems likely that Barry was probably borrowing Iris' car, given that she was homesick from what was hoped to be a bout of morning sickness brought on by pregnancy.