It sounds like you want the actions on the mail server to mimic those within your K9 mail folders, i.e. if you delete messages from your K9 account (gmail) inbox, then the messages in the server account's inbox should move to the server account's trash instead of deleting outright. If that's the case, you might try to MOVE the files to the trash folder instead of deleting them. I tried this for a couple of emails in my local inbox and then logged into my server account and found that they had been moved to the trash folder there as well. If you're using polling instead of push to check your mail then you may have to do a manual poll or wait for the next automatic poll for the files to show up in your mail server account's trash folder.
I don't think K9 supports the option to transfer the files on the server via deletion from your K9 account. The only choices available for deleting local messages are "mark server messages as read", "delete from server", or "do not delete from server" (i.e. leave them alone). Sounds like a feature request you might ask for, i.e. "Move server messages to trash."