Warning: spoilers ahead for Dear Justice League!
Flash's most underrated power makes him essential to the Justice League. Dear Justice League provides insight into the habits of the super team. In one particular segment the Scarlet Speedster shows that he has an extra special way of handling business.
Dear Justice League - a young reader's graphic novel released in 2019 - features questions from children that they have sent to the Justice League. These questions are interspersed throughout a broader heroic adventure and a lot of comedic moments. Each Justice Leaguer is shown answering their e-mails and fan letters - though Flash's method is by far the most impressive.
Created by Michael Northrop and Gustavo Duarte, Dear Justice League includes a couple of kids who want to have a little fun at the expense of the Flash. Keeping in theme with the book, they decide to write the Flash an e-mail. Within it they ask him teasingly why he hasn't responded to the note already since he is so fast and they print it and pin it in their school library. Surprisingly, as soon as they turn around, the Flash is right behind them with their letter in his hand, and he already read it.
Initially it would have seemed like e-mail would be too slow, even for the Flash when it comes to response time. Being a fast person doesn't mean his e-mail is as fast. He still has to receive a notification about it. However, his e-mail clearly operates as fast as he does while he lives up to being the fastest man alive by responding to it so quickly. He is the fastest Justice Leaguer when it comes to answering fans, since everyone else is shown with backed up e-mails or letters. This aspect of his life is one that Flash prioritizes and doesn't fall behind on, even with everything else he has on his plate. This is a very useful thing to do and in many ways, it could make him one of the most essential Justice League members for day-to-day business.
For one thing, Flash is able to keep a personal connection to the fans. This is excellent publicity for the League, while also making him a good role model for the kids he responds to. He doesn't delay in taking care of business. Apart from just being good for public relations, the Flash's ability to be aware of these messages and use his skills to respond quickly is also good for League business. If he is so fast and bills or other important documents are directed towards the Flash, he can make sure they're addressed as quickly as possible. Their bills can be sent in and paid quickly and the Hall of Justice can be kept running with essential tasks being met as quickly and effectively as this response.
Furthermore, if the Flash isn't being bogged down by a backed up inbox, he is able to dedicate more time to other Justice League business. He can keep an eye out for potential dangers they need to take care of. He would also be able to have more downtime to avoid being as stressed out as the other Leaguers when they're checking their e-mails. Additionally, being so on top of his e-mail could allow him to not just receive messages faster than anyone else on the team, but to be able to effectively respond to critically important ones. He could potentially be the easiest Justice League member to contact. The Flash is the fastest man - and fastest mail responder - in the world, making him essential to the Justice League.