I believe the component id for the component that subscribes the current user to a message is "subscriptions.action.add-message-user-email", so you could try adding that inside a custom component using the @component directive:
<@component id="subscriptions.action.add-message-user-email" />
It needs to be in the context of the message you want the user to subscribe to, so you would need to add it to a component that you've placed inside the appropariate "message quilt" (if this is for a forum board, it needs to be in a component that is placed inside the ForumMessage quilt, if it's for a blog board it needs to be in a component that is placed inside the BlogMessage quilt, etc.). If you add it there, you will probably also need to add some CSS to style it to look like a button instead of a link in the post options menu drop-down.
I'm not sure if anyone has tried doing this before, so ymmv.
The other options would be to roll your own subscription component using the REST API call for subscibing the current user to a given message.
If you are trying to add a link/button to subscribe the current user to an entire thread, that uses the "subscriptions.action.add-thread-user-email" component (use <@component id="subscriptions.action.add-thread-user-email" />) and you'll need to place the @component directive in a custom component that is in a "thread page quilt" (ForumTopicPage, BlogArticlePage, IdeaPage, etc.) or else roll your own logic to subscribe the current user to the thread, using the REST API call for subscribing the current user to a given thread.
If you are trying to add the link/button to subscribe the current user to a board, that uses the "subscriptions.action.remove-board-user-email" component(use <@component id="subscriptions.action.remove-board-user-email" />) and you'd need to place the @component directive in a custom compoennt that is in a "board page quilt" (ForumPage, BlogPage, IdeaExchangePage, etc.) or else roll your own logic to subscribe the current user to the board, using the REST API call for subscribing the current user to a given board.
I hope that helps!
-Doug