Storing images locally will definitely speed things up. The initial download of the images may take some time but after they are downloaded, your site should run fast.
You need to set up your directories here: WordPress Admin Area > Tools > Datafeedr > Directories and use the proper placeholder in your URL Settings here: The Factory > Your Store > Store menu > URL Settings. More on that here:
You can simply click the [Set Up] button on the Directories page and that will attempt to create the necessary directories for your images. Once your URL Settings are set up properly using %li and %lt, then your images will be stored locally.