With indoor launderettes, outer layers get spins (6)
I believe the answer is:
'spins' is the definition.
('whirl' can be a synonym of 'spin')
'with indoor launderettes outer layers' is the wordplay.
'with indoor launderettes' becomes 'whir' (I can't justify this - if you can you should give a lot more credence to this answer).
'outer' means to remove the middle letters.
'layers' with its middle removed is 'ls'.
'get' acts as a link.
(Another definition for whirls that I've seen is " Swings or spins round and round".)