Hi Stephanie
Sorry about the issue. It's not really clear in our builder interface but when you use images from Flickr or Google Plus they are referenced from the Story Map, not imported into the Story Map. So if the images are deleted from Flickr or unshared, they won't be available in the Story Map. Accessing pictures from Flickr or Google Plus is really intended to be used when you or someone else are already publicly sharing images via those systems and you want to also include them in a Story Map.
You could upload your images directly into the Story Map Journal builder, which is the easiest way to work with images.
Alternatively you could put them onto a web server and reference them directly via URLs. That can be a good solution if you have a large number of image you want to work with because you can manage them yourself. For example I have 200+ images of San Diego that I use in various Story Maps so managing them on a web server works well because I can reference them via URLs from multiple stories instead of uploading them into each story. The tricky part with doing that, assuming you can get access to a web server or website to put them on, is ensuring that they aren't too large. Unlike accessing pics in Flickr or uploading them, Story Maps don't optimize images you reference via URLs, so you have to be aware of the size recommendations, and if your images are too large to start with it can be a pain to resize them. If you are making a Shortlist or a Map Tour though, referencing your images via URLs is really useful because you can include those URLs in a spreadsheet that you use to author those stories. (Shortlist and Map Tour are place-driven, so they let you define your places in a spreadsheet and generate the Story Map from that spreadsheet.
Hope that helps.
Rupert