You cannot automatically send chat messages, but in this case where you want the user to write a slash command and hit enter, you could maybe convert the input before it gets sent. SyncMotes does the same thing, so it should also work if you react to "/timer" in the same way.
For example you could then send a message that contains some string like "#MyAwesomeTimerAddonName +60" and anyone with the addon who reads that then handles showing the periodic messages on their end.
For long running reminders in guilds it may be better to put them into the MotD or a member note, so offline members also get it when they come online after you sent it the first time. For them to be useful you will also have to put in a relative timestamp that is referring to something every guild member has access to. For example an event in the guild history.