As a renter can I ask my landlord to clean the air ducts?
You can certainly ask. I’d immediately send an HVAC tech out to check your ducts for excessive dust/mold.
If he found none, then no, I would not have your air ducts cleaned. If they were dirty then yesI would have them cleaned.
Now, if they weren’t actually dirty, or the Tech found that the HVAC filter was missing and caused the dust buildup then your next lease would get some very special attention.
HVAC filter replacement (on my leases) is the duty of the tenant. If they remove the filter and dust accumulates in the ducts then they will be getting the cleaning bill.