The Riddler could be a great main antagonist. He could create puzzles and traps that are based on both the Flash's speed and Gotham's dark secrets. For example, he might set up a trap where the Flash has to run through a maze of moving walls in Gotham while also solving riddles that are related to Batman's past.
A new meta - human villain created specifically for the crossover could be interesting. This villain could have the power to control shadows and use them to move quickly, mimicking the Flash's speed in a way. In Gotham, he could use the city's many dark corners and alleys to his advantage. He could also be a master of disguise, fooling both the Flash and Batman. His motives could be to take over both Gotham and Central City and create a new world order where meta - humans rule over normal humans.
In a Gotham Flash crossover fanfiction, perhaps there's a device that disrupts the speed force and it's located in Gotham. The Flash has to go there to fix it. He meets the various characters in Gotham like the Joker, who tries to use the Flash's powers for his own chaos. Meanwhile, Flash has to work with the likes of Gordon and Robin to stop the Joker and repair the device. The different moral compasses of the Gothamites and the Flash could lead to some interesting character interactions.
Perhaps there's a villain in Gotham who has discovered a way to siphon the Flash's speed force. The Flash has to go to Gotham to stop this villain, and in the process, he meets the various characters of Gotham like Gordon and Catwoman. They all have to work together to not only stop the villain from stealing the speed force but also from using it for some evil plan in Gotham.
When Savita explained the concept of time travel, he meant that time travel was a way to travel through time, and time travel referred to a way to extend the state of a timeline from one moment to another in order to avoid the paradox and uncertainty of time travel. To be specific, time travel could directly change the state of the timeline through the occurrence of an event or the entry of an entity, thus avoiding many common problems and contradictions in time travel.