When adding an image into your email signature you will need to have a DIRECT LINK which means you will need to adjust the public link Dropbox gives you access to.
Instructions on how to change a Dropbox Link:
Copy Dropbox link of the image file that you want to share. (Right click on image file in your Dropbox folder and choose Copy Dropbox Link). You should have something similar to this: https://www.dropbox.com/s/tg0cfa565aue4ak/zoo.jpg?dl=0
Just delete the 0 at the end and replace it with a 1: https://www.dropbox.com/s/tg0cfa565aue4ak/zoo.jpg?dl=1
Visual Steps
1) Click the "Insert Image" icon:
2) Add the public link from Dropbox:
3) Change the 0 at the end to a 1:
4) If you made the change correctly, you'll see the image when you click "Insert":
