i have more than 5000 products in my magento shop, since a week, all newls uploaded products dont have an image because of the missing browse and upload button. As well, under pages im trying to insert media and same problem.I have Magento ver. 22.214.171.124, Google Chrome Version 55.0.2883.87 m and adobe flash player is enabled.
I had a similar issue in my installation and I found the following link solved the problem.
You can always double check to make sure Chrome's Flash plugin is enabled