How to use support FileProvider for sharing content to other apps?

Using FileProvider from support library you have to manually grant and revoke permissions(at runtime) for other apps to read specific Uri. Use Context.grantUriPermission and Context.revokeUriPermission methods.

For example:

//grant permision for app with package "packegeName", eg. before starting other app via intent
context.grantUriPermission(packageName, uri, Intent.FLAG_GRANT_WRITE_URI_PERMISSION | Intent.FLAG_GRANT_READ_URI_PERMISSION);

//revoke permisions
context.revokeUriPermission(uri, Intent.FLAG_GRANT_WRITE_URI_PERMISSION | Intent.FLAG_GRANT_READ_URI_PERMISSION);

As a last resort, if you can’t provide package name you can grant the permission to all apps that can handle specific intent:

//grant permisions for all apps that can handle given intent
Intent intent = new Intent();
intent.setAction(Intent.ACTION_SEND);
...
List<ResolveInfo> resInfoList = context.getPackageManager().queryIntentActivities(intent, PackageManager.MATCH_DEFAULT_ONLY);
for (ResolveInfo resolveInfo : resInfoList) {
    String packageName = resolveInfo.activityInfo.packageName;
    context.grantUriPermission(packageName, uri, Intent.FLAG_GRANT_WRITE_URI_PERMISSION | Intent.FLAG_GRANT_READ_URI_PERMISSION);
}

Alternative method according to the documentation:

• Put the content URI in an Intent by calling setData().
• Next, call the method Intent.setFlags() with either FLAG_GRANT_READ_URI_PERMISSION or FLAG_GRANT_WRITE_URI_PERMISSION
  or both.

• Finally, send the Intent to another app. Most often, you do this by calling setResult().

  Permissions granted in an Intent remain in effect while the stack
  of the receiving Activity is active. When the stack finishes, the
  permissions are automatically removed. Permissions granted to one
  Activity in a client app are automatically extended to other
  components of that app.

Btw. if you need to, you can copy source of FileProvider and change attachInfo method to prevent provider from checking if it is exported.