How to do it
1. Get a Slack Webhook URL
Get a Slack webhook URL to use Slack API.
See Sending messages using Incoming Webhooks - Slack API
2. Create a shell script posting a message to slack
Create a shell script like below and give +x permission to the receiving user.
3. Add a recipe to .procmailrc for executing the shell script
The example .procmail is like below.
Procmail executes the shell script when receives an email and forward the email to $MAILDIR