Find the gallon load of the washer, some are 15 gallon loads. Your have 4 so four times the load. If it takes 3 minutes to fill, there are 60 gallons divided by 3 for 20 gallon loads. If the tankless coil is going to be kept at 180+F and the temerature necessary for a washload is 120F, that is approximately 1/2 the rise from 50F to 180F, so the tankless is required to give 10 gpm while combined with a mixing valve providing 10 gpm of cold water for the mix. This requires a 500,000 output btuh of boiler for the first hour draw, 700,000 btuh thereafter on continuous draw. The load can be spread by drawing on a 120 gallon tank for the smaller boiler size.
The large boiler size above is required if you must draw all four washing machines at the same time, if you can guarantee that the washers won’t be filling at the same time and not more than 4 times each hour, then you can have a small boiler. A large storage tank can make the process less dependent upon timing.