If you make the data file available from your account and provide the URL, they should be able to CloudImport it. For example, I made some example data publicly readable:

data=CloudImport[CloudObject["https://www.wolframcloud.com/obj/jfklein/financialtimeseries.csv"]]

If you don't want to make the data files available to just anyone, you can use Permissions on the object to control that. Give a single user access to a cloud object obj:

SetPermissions[obj, "alice@example.org" -> "Read"]

Or a group of users:

SetPermissions[obj, {"alice@example.org", "bob@example.org", "charles@example.org"} -> "Read"]

Or you might want to create a PermissionsGroup, grant read to the permissions group, and then manage the permissions group membership separately (AddUsers and RemoveUsers, listing with pg["Members"]. This probably will work well for you if you have multiple objects that you want to get the same permissions.