This works whether or not you still have the app installed.
If you still have the app, or any IRC client, connect to irc.ircly.net, identify with your nickname and password, then run:
/msg NickServ DROP
This immediately removes your registered nickname and its associated account data — password, saved preferences, friends list, and any other data tied to the account. This action can't be undone.
If you've uninstalled the app, forgotten your password, or would rather not use the command above, email a deletion request directly:
Email a deletion requestInclude the nickname you registered so the right account can be located and removed. Requests are handled directly by the person who runs ircly — this is a small, independently-run network, not a large company with an automated pipeline, so it may take a short time to process, but it will be handled.
Chat messages sent to public channels are, by nature of IRC, already visible to whoever was present at the time and aren't retroactively removable from other people's clients or logs, the same way a spoken conversation can't be unheard. Anything ircly itself stores under your account — as listed above — is what this deletion request removes.