I have added both the link to my book and a link to the image, but I still cannot get the image to show up. How do you do it?

I tried cutting and pasting my code in, but it sent the html into orbit :)

The simplest is as follows:

Use the ribbon at the top of your Edit Signature box to add a picture, using the picture icon (little mountain and a tiny dot of a sun symbol - sorry, not sure how comfortable you are with these tools so I am breaking it down fine.) Insert the link to your image, which I believe is https://www.royalroadcdn.com/covers-full/the-scarlet-demon-aacamnzybw8.jpg  in your case. 

Once that's done, select the resulting HTML that got cranked out by the system into your signature, and then select the Insert Link tool, which you used to insert the link to your book.

That will put in both the cover and allow people to click the cover to get to the link, I believe (it's been a couple of months since I did mine.) Give us a shout if that doesn't work. 

If you want something more complex, such as a linked cover and a text on the side, I can pm you the code I used for mine, which is a table. It looks nice, except on phones where the image gets squished ^^; I'm sure that's fixable, but I can't be bothered to troubleshoot for now. Others may have other suggestions. I also found a handy FAQ on html-royal-road flavour, I'll try to find it in my bookmarks.

I found an old post of someone who explains it better than I can  :) This is for the basic picture-with-link-to-story. 

https://www.royalroad.com/forums/thread/105985

Thank you so much! That really helped.

If you want to get more in depth or need to add additional books and the like (or anyone else that comes across this post w/ a similar question), I wrote a pretty expansive post on the subject that's pinned in the Self Promotion subforum:

https://www.royalroad.com/forums/thread/107061