"barrage of emails" is correct and can be used in written English. You can use it when referring to a large amount of emails received at once. For example, "I received a barrage of emails in response to my advertisement.".
Steven says: The resulting barrage of emails and tweets we received was a little overwhelming.
There is a non-stop barrage of emails throughout the night and weekend asking for work.
In a bid to steal the narrative, both campaigns sent out a barrage of emails to reporters both during and after the debate.
The most successful colleagues probably look like they can effortlessly manage a constant flow of messages, invitations to purposeless meetings, and a barrage of emails at all hours of the day.
In addition to the usual run of "clever headlines" in the tabloid pres (this one's not quite so clever, but is technically true), Terence has also been on the receiving end of a barrage of email from some well-meaning Christians offering a little constructive criticism of his work.
His story about Obama paying to keep a Muslim museum open during the government shutdown last year fooled Fox News, and when he wrote that "Argon Elementary School" in San Francisco was suspending a fourth-grader for saying "Merry Christmas," the real-life Argonne Elementary in the Bay Area received a barrage of email tirades, angry phone calls, and "veiled threats of violence".
One of the brochures had bullet points that read, "$$$ - No limit on income," "Highest paid people in the world are salespeople" and "Top 20%% = Never worry about $$$." White boards displayed around the office tracked each recruiter's performance, and managers sent daily barrages of emails questioning why enrollment targets weren't being met.
Thanks to Ludwig my first paper got accepted! The editor wrote me that my manuscript was well-written
Listya Utami K.
PhD Student in Biology, Bandung Institute of Technology, Indonesia