I would like to create a small security camera network utilizing devices I already have, namely Android phones. All phones can have a constant sources of charge, as well as be attached to my wifi network, which has a custom NAS attached. I understand there are already apps that will stream to a Google Drive, however my lack of bandwidth makes this quite unappealing. Are there any apps that will allow me to do this that I haven't found, or are there any recommendations for creating an application that will allow me to do this.
You could try using IP Webcam, installing the computer driver on a computer on a LAN, and then using PC webcam software that points at your NAS. Not sure on how to write directly though. If your NAS allows you to host an FTP server from it, however, you could write directly.
On the topic of FTP, you could use Filezilla Server on a Windows computer, and point it at your NAS, if you didn't want as much overhead, although if you are usiing the lite version you will get a watermark in this mode.