Instagram allows you to retrieve the URL of public-facing posts so that you may share your photos on other platforms. This method is limited to public-facing posts. Posts that are classified as "private" may not be shared.
Open Instagram, and browse for the photo of your choice. Once found, select the Menu button located under the photo (3 vertical dots). Then, select Copy Share URL:
A message will be displayed to confirm that a sharable URL has been copied to your clipboard.
Image: © Instagram.