There is a Kindle app for Chromebook I am fairly certain. Definitely is one for PC to download.
I would grab that app for your Chromebook. Follow whatever steps are necessary launching it to link it to your Amazon account. Then any purchases will automatically appear in the app for you to download.
Thanks! I wound up downloading the Kindle app on here, but the kindle app doesn't seem to play nice with the size of these books. However downloading the Kindle app allowed me to buy them at all, and now when I go to Comixology they're all there and I can read them that way which is probably my preferred method anyway. Kind of a bit convoluted, I was expecting to be able to just buy them and have them show up on my Comixology account if I was signed in through Amazon.
Because I am a total sucker for Star Wars I picked up all of the new/canon graphic novels they had available outside of the C-3P0 one-off which I might still get out of curiosity. The haul for what I think was $43.60:
Star Wars Volumes 1-5
-Darth Vader Volumes 1-4 (entire run)
-Star Wars Kanan Volumes 1-2 (entire run)
-Star Wars Poe Dameron Volumes 1-2
-Star Wars Doctor Aphra Volume 1
-Star Wars Princess Leia (entire run)
-Star Wars Lando (entire run)
-Star Wars Chewbacca (entire run)
-Star Wars Han Solo (entire run)
-Star Wars Vader Down (entire run)
-Star Wars Shattered Empire(entire run)
-Star Wars Obi-Wan & Anakin (entire run)
Fucking ridiculous.