For HTML email (and therefore MailChimp):
- The images need to be hosted somewhere. That could be MailChimp or another online hosting service.
- The URLs coded in the HTML need to be updated to point to those online locations: http://www.blahblah.com/something
Creating properly coded HTML emails is not a push button process. There are a lot of details involved. While similar to creating websites, emails have their own unique issues. This isn't a simple thing of you doing something wrong, you just need to spend more time learning about all the intricacies of HTML emails.
As I said previously, even if you get the images working, it's very likely the code generated by Photoshop will not work in a wide variety of email apps. It was made (long agao) for webpages and I don't recommend using its code.
To get this working properly could require coding the email from scratch yourself, or redesigning the email using a MailChimp template and filling in the images you create in Photoshop into their template. MailChimp templates are responsive (meaning they adapt and look good on multiple screen sizes). A single design from Photoshop will not be ideal on both phones and desktops.
In other words... this is not the best approach to designing an HTML email but maybe if you upload your images you could get it working 🙂