For China to launch a Progress, one of two things would have to happen:

1. China adapts the Progress vehicle to their booster. This is often a lot more difficult than it seems, given that the Progress was specifically designed for launch on the SL-04 (Soyuz) launch vehicle. Adapting it to launch on a Long March would require China to worry about electrical interfaces, vibration characterists, and a host of other factors. They'd also have to work out purchasing or licensing agreements with Russia, build the payload processing facilities, and either develop their own mission control center for the Progress vehicles or hire the Russians to do the job. Somehow, I doubt they'd be interested in doing that, especially if the orbital modules/space station has military purposes.

2. China develops the infrastructure to launch Progress vehicles on Soyuz boosters from their territory. This would require then to purchase (or license) the boosters and vehicles from Russia (with whom they have not always enjoyed warm relations), build payload and booster processing facilities, launch pads, and transporter/erector systems.

If China wants the capabilities of the Progress, perhaps the most straight-forward approach would be for them to develop their own version of the vehicle like they did for their manned spacecraft. They may choose to adapt, license, or purchase Russian technology (a very good idea) or to roll their own. Japan has tested automatic docking technology. Europe is developing their own version of resupply vehicle for the ISS. China could do the same for a reasonable cost, especially if they licensed proven technology from the Russians.