While The Flash is a superhero show, it is also about the human aspects of the characters rather than just being about their abilities and how they use them to save the world... and that means romance.
Almost every member of Team Flash has been in a relationship at some point that has motivated their actions and affected the decisions they have made, for better or worse. While some relationships have been able to survive all of the things the show has thrown at them including time travel, alternate Earths, and even death, others just weren't destined to last.
Cisco and Kendra
Kendra Saunders was a barista at Jitters that Cisco began dating after being convinced by Barry to ask her out. Their relationship hit a road bump when she was later attacked by Vandal Savage, and Carter Hall (aka Hawkman) came to her, revealing that they were immortal soulmates and that she was the hero, Hawkgirl. After Team Arrow and Team Flash defeated Savage, her relationship with Cisco came to an end and she had to leave Central City for her own protection, eventually boarding the Waverider and becoming a Legend.
Barry and Linda
Barry met Linda Park when he and Caitlin performed karaoke at a bar and decided to break up with her after learning that Iris had feelings for him. They dated for a short period and Barry even revealed that he was the Flash to her in order to further the trust between them but after she's attacked, Linda ends up moving to Coast City to protect herself from both Zoom and Doctor Light, her Earth-2 doppelganger.
Cisco and Gypsy
Cynthia, aka Gypsy, was a bounty hunter from Earth-19 that Cisco met when she came to Earth-1 looking for H.R. Wells and he challenged her to a trial by combat to spare H.R. which he ended up winning. After later helping the team with Gorilla Grodd and Solivar, she kisses Cisco before going back to her Earth, marking the start of their relationship with them both often switching back and forth between Earths to visit each other. She later offers Cisco a job on Earth-19 so that they could be together due to the long-distance being difficult on both of them but he ends up declining and they end their relationship.
Iris and Eddie
Despite her initially not being a fan of him, Iris started dating Eddie Thawne, her father's partner, during the months when Barry was in a coma after being struck by the lightning that would give him his powers. Their relationship was moving pretty fast and after some time the two moved in together with Eddie even planning to propose to Iris.
However, Eddie keeping Barry's identity a secret from her put a strain on their relationship but they ultimately reconcile. Unfortunately, their relationship ended when Eddie shot himself in order to prevent Eobard Thawne from killing team Flash and protect the city shortly after learning that he and Iris wouldn't end up together.
Wally and Jesse
Wally initially rejected her advances, knowing that she would have to return home, but he eventually changed his mind and began dating Jesse Wells. Jesse remained on Earth-1 while Harry returned to Earth-2 but eventually moved to Earth-3 to take over for Jay Garrick after he took Wally's place in the speed force which made their relationship more difficult even though Wally would often visit her. After a while, Jesse sent a break-up cube to Wally and after one last visit, they agreed to end the relationship which led to part of his decision to take a break and leave Central City. He later dealt with his unresolved feelings on Legends of Tomorrow when the death totem was used to present him with a vision of her allowing him to move on.
Barry and Patty
Patty Spivot joined the Central City Police Department as a member of the member of Anti-Meta-human Taskforce in hopes of getting her revenge on the Mardon brothers for the death of her father. After she and Barry had been working together for some time, he asks her out on a date and the two began a relationship. After realizing that Barry was keeping a secret from her, she realized Barry was the Flash. Patty asked him to tell her saying that if he did, she would remain in Central City instead of going to college in Midway City to become a CSI but Barry refused. Her suspicions tricked him into using his powers before she left for good.
Ronnie and Caitlin
Ronnie and Caitlin met each other while working at STAR Labs and got engaged after a few years of dating. Their relationship came to a tragic halt the night the accelerator malfunctioned and exploded, with Ronnie getting caught in the blast. Caitlin believed he had died, only to later learn that he was still alive had merged with Professor Martin Stien, becoming Firestorm. After the team learned how to separate Stien and Ronnie from each other, they both joined Team Flash as members and Ronnie continued his relationship with Caitlin and the two eventually got married. However, the marriage was short-lived when Ronnie died while closing a singularity that opened over the city, once again separating them.
Cisco and Kamilla
After splitting from Gypsy, Cisco met photographer, Kamilla Hwang, at a bar called the Liquid Kitty where she worked. After they had been dating for a while, Cisco made the decision to tell Kamilla about his secret identity, revealing himself as Vibe.
To his surprise, she ended up being extremely supportive and even became an ally to Team Flash, occasionally helping out as mission control at STAR Labs. Kamilla became trapped in the mirror dimension along with Iris which devastated Cisco, leading him to travel to Atlantis in order to try and figure out how to give Barry his speed back so she could be saved.
Joe and Cecile
As a District Attorney, Cecile Horton began to work closely with Joe on several of his cases, leading the two to eventually start dating. Joe eventually revealed to her that Barry and Wally were the Flash and Kid Flash and she became an ally to the team. She then moved in with Joe during the time when Barry was stuck in the Speed Force and revealed that she was pregnant, later giving birth to a baby girl that they named Jenna. While they aren't currently married, Nora seemed to indicate that they eventually would be.
Barry and Iris
Any fan of The Flash knows that Iris West and Barry Allen are the main relationships of the series. The two always shared a strong connection and secretly had feelings for each other, their relationship wouldn't be fully explored until Barry returned from the Flashpoint timeline and admitted he loved her. After dating for months, they moved in together and eventually got engaged. After their official wedding was interrupted, they had a do-over double wedding with Oliver and Felicity that was officiated by Diggle.