Downloading list of images
I think this is pretty good code!  I have only a few minor suggestions:


Rename image and images to something that makes clear they are URLs, not files, not numpy ndarrays, and not any other format.  Maybe image_url and image_url_list?  The first time I read the code I didn't know what they were.  Your docstrings are good, but IMO, its even more Pythonic to have your code speak for itself (with docstrings present as backup obviously).
It took me several times of reading the code to figure out exactly what need_reload_file is.  Could you name it to be more descriptive?  Maybe failed_image_urls_file or something?
Web programmers might know what various request status codes mean, but in case a web noob like me reads your code, a comment explaining the meaning of r.status_code == 200 would be helpful.
I don't understand the file_name.split('=')[-1] bit.  What constraint are you assuming about the structure of file names?