I've got the sync happening every 24 hours but it doesn't look like mailing addresses are syncing from MailChimp to Salesforce.
After a quick review of the Sync Profile, I found that the Step 4 Field Mapping just needs to be set up for Address fields (5) to map back to Salesforce for new records.
So you need to use the following mapping:
Address -> Street
City -> City
State -> State
Postal Code -> Zip
Country -> Country
MailChimp Address field is quite strict so usually I always suggest to users it is better to use a text field for each address component 5 merge text fields for street, city, state, zip and country.
If you're needing subscribers to be able to update their existing address in Salesforce from MailChimp then after mapping the fields just select in Step 2 this feature below.
*Update Salesforce.com if subscribers update their profiles in MailChimp
This will use mapping configuration to update data. Please make sure you configure the mapping correctly.
A webhook will be setup in the specified MailChimp list by SyncApps if this option is enabled.
The 5 fields must be mapped rule is only applied if you are using ADDRESS data type field in MailChimp.
If you use a text data type field then the above rule is not applicable. You can sync city only if needed to a city merge field (with text data type).
Address data type can be distinguished in field mapping with "MERGENAME-city, MERGENAME-country, MERGENAME-state, MERGENAME-address, MERGENAME-zip" like in the following screenshot.
As Billing City is a custom field please send us the custom field details of it through email@example.com.