Outlook uses Word to render the images, and Word does not support embedded (src="data:image") images. You need to attach the image as a file, set the PR_ATTACH_CONTENT_ID property on the attachment (Attachment.PropertyAccessor.SetProperty), and make sure your HTML refers to the image through the src=cid:xyz attribute (where xyz is the value of the PR_ATTACH_CONTENT_ID property).
PR_ATTACH_CONTENT_ID property DASL name is http://schemas.microsoft.com/mapi/proptag/0x3712001F