If I hosted a few files on the NXT's Decentralized Data Straoge Cloud, how can I access those files via an API?
You can download your file using this API
localhost:7876/nxt?requestType=downloadTaggedData&transaction=nnnn&retrieve=true
where nnnn = Txid of your uploaded file
You can search txid for all your uploads using requestType=getAccountTaggedData&account=NXT-XXXX-XXXX-XXXX-XXXXX
where NXT-XXXX-XXXX-XXXX-XXXXX is your account number
If your localhost is not hosting prunable data, retrieve from a public node which is a Service Provider (with PE & AI listed under Services) in your peer's list.
Examples:
Retrieve all Txids of all uploads for account NXT-TBAJ-LVLX-YCWY-5FRLD 23.94.134.161:7876/nxt?requestType=getAccountTaggedData&account=NXT-TBAJ-LVLX-YCWY-5FRLD
Download PGP key of Core Dev http://23.94.134.161:7876/nxt?requestType=downloadTaggedData&transaction=633908232195174623&retrieve=true
Full set of API for Nxt Data Cloud can be found at localhost:7876/test?requestTag=DATA