bombard (someone) with emails

Translations
заваливать (кого-то) электронными письмами
The customer service team was bombarded with emails after the product launch.
Команда службы поддержки была завалена электронными письмами после запуска продукта.
Definitions
To overwhelm or inundate someone with a large number of emails, often to the point of causing frustration or difficulty in managing their inbox.