I know of no way to get a dialog launcher button itself through the Interface. You can include an existing group on your tab
that already has the dialog launcher you want. I don't believe you can edit the group, but you can add other custom groups to the tab.
For serious projects or something that will be shared, I would always recommend using an XML editor. Here are three resources:
Below is a custom tab created through the interface where I simply added the Styles Group from the Home tab. Perhaps that is what you want.
It includes the dialog launcher for Styles that gives you the Styles Pane.
BTW, you may find the gallery under Quick Styles Gallery. (just a guess)