LogBrowser is disabled 6.5 onwards and is not longer available in Flex/H5 client. This was made as part of the last set of improvements of the Flex Client prior to 6.5 GA. Log browser was removed and is not available afterwards.
Feature is not part of vSphere Client (HTML5).
Official documentation to be updated very soon on VMware websites. Tentative dates for the documents and articles to be updated is post the release of vSphere 6.7 U1.
Hence, this post concludes that though the feature might work on a few builds of vSphere 6.5 - they are not officially supported.