As mentioned in the comments, the alerts in SharePoint are per user, so you are not attempting to "subscribe for the same alert", but instead to "subscribe for a new alert".
If you want to create a custom button the users can click to subscribe for specific list, create your HTML button with a link to the following URL:
In this URL the
ID is the ID of your list. You can rather easily get this URL by accessing to
https://sharepointsite/_layouts/15/SubChoos.aspx, selecting the wanted list and clicking Next. The URL on the following page is what you are looking for. Note that if your list is on a subsite, you should adjust the URLs to include the path to the subsite.