Most macro photography enthusiasts will laugh at anyone using the built-in flash that comes with plenty of consumer-level cameras, with good reason, in most cases. I agree that if you are serious about macro photography then you should seriously consider buying a ring-flash setup. The problem with these are is that they are expensive. For example, expect to pay around £250 for the The Metz Mecablitz 15 MS-1 Digital Ring Flash. For a more professional level kit you will need to pay between £500 and £1,000!
However, if you only take the occasional macro shot then there may be occasions when using your camera’s built-in flash to help improve your shots. It does depend on your model of camera though as not all built-in flashguns can cope with subjects close to the camera. Also, some macro lenses are quite long when shooting macro and you may find the flash is so close to the camera body that you end up with deep shadows cast across your subject. However, if you have the Sony a6000 you are in luck, as the flash extends a fair distance above the top plate of the body. In my experience this means that you can get away without casting a deep shadow across your subject, depending on how far your lens extends.
Here are a couple of images showing the difference that flash can make. The first was taken without flash, the second with the benefit of the built-in (tiny) flashgun on my a6000. Both images were taken using a vintage lens, in this case the Tamron 28-70mm 3.5-4.5 lens (in this case a Minolta MD fit, attached using a K&F Concept adapter). Both were taken hand-held at 1/90 sec, F8 and ISO 800.
I think you will agree that the second image (with flash) is the better of the two. Both have had the same corrections applied for noise reduction and been tweaked for exposure levels. The first image, due to the lack of flash is much more noisy and I would argue, is less sharp, even though I had to use manual focussing for both images as I was using a manual lens with an adapter that doesn’t allow auto-focus.