You probably have solved it by now, but for the benefit of everyone else searching in the future, this post solved it for me: Update: Authenticated Access to S3
Specifically, this curl command gave me everything I needed to make it work:
curl -H "Authorization: OAuth oauth_consumer_key=\"{{key}}\", oauth_token=\"{{token}}\"" https://api.trello.com/1/cards/5e839f3696a55979a932b3ad/attachments/5edfd184387b678655b58348/download/my_image.png