My clothes would be "meine Kleidung." I'm not sure if there is a singular for clothes but my dress is "mein Kleid" (nt.) and my dresses is "meine Kleider" (pl.) which does look rather similar to clothes.
What about "my clothes are in the washing machine"? Wouldn't that be "meine Kleider sind in der Waschmaschine"? Doesn't 'meine Kleidung' mean 'the garments I'm wearing', whereas 'Kleider' refers more to individual items of clothing?
If the singular 'das Kleid' is neuter, it would stand to reason that the plural 'Kleider' is also neuter. But I know that many language facts don't stand to reason, so I could be very wrong. Does the fact that it's plural make a difference?