I recently bought a HDMI to DVI cable for my monitor which takes VGA input. It works fine with windows on laptop. In raspberry pi, it "blinks". The screen goes off and again the pre-built logo animation of the monitor. In ubuntu, the screen is sometimes supported, sometimes, it also "blinks".
I think you are out of luck. A DVI cable has lines for both digital, and analog signal. The Pi will only send data over the digital lines, while you monitor (being a VGA monitor) only listens to the analog lines.
DVI cables are kind of weird in that way. The can even carry USB signals.
Probably too late for OP, but try config_hdmi_boost=4 or even config_hdmi_boost=7. This tends to improve blinking issues.
You can change this by editing config.txt:
sudo nano /boot/config.txt - for more info see this.