I just purchased an apple lighting sd card camera reader

The SD Card Reader is one way. From SD card TO iPhone or iPad. Not FROM iPhone to SD Card reader.

You'll need to either email the videos to yourself, or connect your iPhone to your home computer and upload the videos to your computer, then use your computer to download them to SD Card, assuming your computer has SD Card capability (most modern computers do, these days). Or, if you use iCloud Sync, you can access the content on your computer by signing into iCloud on your computer.

Here is a link which explains how to upload content from iPhone to Computer --> Transfer photos and videos from your iPhone, iPad, or iPod touch - Apple Support