mDNS is a broadcast thing, so if it's on your network and your router doesn't filter broadcast (some do) then it should work.Like I said earlier, I get to flash fine with BrewFlasher. I can access it, use my Smartphone and configure it. Although I put an mDNS name, it seems that it is not registered. I can locate the device in the list of devices connected to my router using the MAC address (I have more devices with the ESP label… they are sonoff devices for the lights in the house.) I don't know if it is normal that the mDNS label is not recorded.
If you are using Windows, try zeroConfServiceBrowser. It should show all of the devices broadcasting on your network. These days there should always be at least a few. If you see none, then the problem is either your computer or your network. Are you able to connect to your Raspberry Pi by name? Can you ping your ESP device by name from the Pi?