It's possible for HDMI to blink but here we have a display with 2 HDMI, DisplayPort and maybe some other.
Try the other HDMI and be sure when dealing with HDMI to power off the display, unplug the HDMI and AC for 10 minutes to get the HDMI chips to reset. And of course have the video settings in a supported range.
Just got his refurbished Dell U2715H out of the box and plugged in. For the first few minutes it was fine, then the display would go black for a second or two, then come back. It may flash like this 5 times, then stop for a minute or two with a normal display, then start back up again. I downloaded the latest monitor driver with no change. And the smaller Dell S2340M I'm upgrading from works fine. I'm running Windows 7 64 bit on a Dell OptiPlex 7010 Service Tag: 2P4YCX1 Any suggestions before I return it?