Carl,
Hello and good morning! My name is Joe and I work in Esri Support Services.
I did a quick search online and found this previous GeoNet Post (https://community.esri.com/thread/202338-arcgis-online-sort-attachment-in-ascending-order). According to the response from Mike, there is currently no way to rearrange attachments in ArcGIS Online.
I also did a quick search through our internal resources and found an already existing enhancement regarding this functionality. This enhancement is titled ENH-000119843: Provide the ability to sort or rearrange attachments shown in pop-ups in ArcGIS Online's map viewer. This enhancement was recently submitted (February 2019) and it's still marked as New.
If your maintenance allows you access to Esri Support, I would recommend that you create a case with us and request to be attached to this enhancement. That way, you'll be able to track it via MyEsri and see if there are any updates on the enhancement!
Feel free to reach out with any additional questions.
Joe
