Get a list of attachment ID's for each Work Item on VSTS
You asked the similar question before but not give any feedback.
To make sure this issue clear. I will answer it again.
To get the attachment id you can use the Get Work Item API with $expand=all
:
https://dev.azure.com/{organization}/{project}/_apis/wit/workitems/{workItemID}?api-version=5.0&$expand=all
Then you will get the attachment ID in the url in the relations section (I use the tool postman):

So, you can get the attachment ID is acd5af0e-c015-4e8f-8354-a6858582deb2
.
BTW, you could download the download the attachment use the API:
https://dev.azure.com/{organization}/{project}/_apis/wit/attachments/acd5af0e-c015-4e8f-8354-a6858582deb2?api-version=5.1-preview.3
Ticket: Attachments - Get
Hope this helps.