When trying to install the Indesign plugin from the Adobe Exchange, you search for the Xinet plugin for your Adobe software (For example, Xinet Plugin for CC 2020 Indesign) and click the "Free" button. No information about the plugin appears, and the installation never starts.
As an initial first step, verify that this is not isolated to your Web Browser by attempting to download the plugin using a Private Browsing session or alternate Web Browser. If the trouble is not reproducible, you can clear your Browser's cache and cookies.
If the trouble persists, you can request that another user access the plugin using their Adobe account. If they can access the plug-in, the problem is likely related to your Adobe Client ID. You will need to reach out to the Adobe Support team for them to resolve the issue directly.
If the other user cannot access the plug-in either, please open a support ticket with Xinet Support.