Make sure to use an older Kindle for PC version. I think I have 1.26. With that version you also need the KFX input plugin.
With the plugins installed, you should be able to drag the files you downloaded with Kindle into Calibre and have it detect them.
The next step is conversion. Be very careful here, Calibre likes to fuck with images. You’ll probably want EPUB as the target format.
Set the target device to Tablet, or your images get resized.
Also disable the title image resizing in the last register.
I’d recommend you set these setting as default, so you don’t forget changing them.