You would have to encourage Adobe to incorporate iCloud functionality into InDesign. Currently it has no iCloud integration whatsoever. Presumably Adobe would prefer you to pay to use their own cloud storage offering (Creative Cloud).
iCloud itself does not have a general purpose file storage facility for arbitrary files. Each individual app or program needs to support the iCloud APIs to allow saving and loading of files directly to and from iCloud.
There are a number of general cloud solutiuions that Mrs Miggins refers to.
Here is a recent review article that you might find useful.
Cloud Services Compared: Google Drive vs. Dropbox, SkyDrive and iCloud
Hope this helps get you started