Airmail has this feature to send your mails and archive them upon sending the message. This will let you remove the particular conversation from the Inbox to reduce the clutter after you have replied to it. This helps in achieving Zero Inbox.
You will need to enable it in your Airmail’s preferences. You can see the option in Preference > Composing and then tick 'Use Send and Archive' option as illustrated below:
Once you have selected the option, you can easily 'Send and Archive' when replying.