Depends on what you mean by “access”: You can’t use the ones for the existing tools (though I think you can trigger them for the existing tools if you need that), but you can write your own. You do this by registering actions, and then listing those as the toolbar actions for your tool.
You can even use the existing icons by setting the icon to ":path-to-icon" (note the leading :), e.g. ":images/32/flip-horizontal.png". You can browse the images that come with Tiled, and which you can reuse, here.