I'm trying to upload a shapefile on arcgis.com but I'm always getting an error (Timeout exceeded). I'm having an 30 days trial account, maybe this is causing the problem?
Here you can download the shapefile which I've been trying to upload
The problem is that your data contains multipart features. Try to upload the polygons from Desktop by creating a Feature Service instead of uploading the shp. I tried with your data and it worked.
- Go to File >> Sign In and use your AGOL credentials - Go to File >> Share as >> Service - From Capabilities choose Feature Access