There are laundry rooms at each DVC resort and the washers and dryers are free for DVC members. Access to these DVC laundry rooms are controlled by locks which can be opened with your MagicBand (Note: Its not uncommon to find the laundry rooms are not locked.)
By the way, Disney resorts that have a hotel component and a DVC component, like AKV Jambo House, often have separate laundry rooms. At Jambo, the DVC laundry room is on the 5th floor at the start of the Zebra trail (near villa #5408). Jambo House has other laundry rooms on the 1st and 2nd floors, but those are used by hotel guests and are not free to DVC members.
Another tip: Laundryview.com, the app that lists all the laundry rooms at Disney by resort. But the Jambo House DVC laundry room on the 5th floor is erroneously listed under "Animal Kingdom Lodge Kidani Village." If you intend to use the app to track availability, remember to click on Animal Kingdom Lodge Kidani Village to find the Jambo House DVC laundry room. Make sense?