I just got a new Raspberry Pi 3B+ with the official case and official power supply. When up, I get a blinking red LED, and on the screen (HDMI) I see a big rainbow-ish square and a lightning symbol in the top right corner of the screen.
I am using a Kingston 16GB SD card with Raspbian Stretch Lite on it.
From what I've read, the lightning symbol means there isn't enough power, but my other Pi's (e.g. Pi zero) work fine with the supply (though I know the Pi current draw is much lower than the 3B). I get the same problem with the 3B if I use the SD card from the Pi zero.