Blogger can access any image in your Google Album Archive, which includes all images uploaded to Google through Google Photos, Google+, Hangouts, Blogger, Google Drive and other Google services (Learn more about Album Archive).
How to insert an image shared to Google+ or Hangouts into a Blogger blog post
1. Sign in to Blogger with the same Google account you use to sign in to Google+ or Hangouts
2. Open the Blogger post editor and click the Insert Image icon
3. On the Add Images options window, select the From Google Album Archive tab
4. To insert an image you shared in a Hangout chat, click on the Hangout name, then the image to insert
Each Hangout chat has a separate album, titled Hangout: [name]
You will only be able to see an insert images that you shared in the chat, not anyone else's images.
5. To insert an image you shared on Google+, click Photos from Posts
Images are arranged in chronological order by upload date.
6. Click on an image to select then click the blue Add Selected button to insert the image into your blog post.
Watch the video showing how to insert images from Google+ and Hangouts into your Blogger blog post
Learn more about how insert photos and videos into a Blogger blog post in the Blogger Help Center.
For more tips on how to go beyond plain text in your Blogger blog post, watch my free webinar: Blogger: Beyond Text with Michael Daniels.