When I close the viewfinder, red light keeps blinking.

Is the battery door maybe not closing tightly, causing the metal area that touches the tips of the batteries to not be in close enough contact with them? This happened with my camera due to a cracked battery door, and until I can afford to replace it, I've put a rubberband around my camera over the little door to hold the batteries in tightly! Surprisingly, this is working for me! I know it's not an optimal fix, but thought I'd offer the suggestion. (You didn't say what make/model your camera is.)

Try these procedures.

I did this to my car once. Be sure the latch isn't closed as you are trying to close the trunk. With the trunk open pop the trunk once, then see if the trunk latches properly.

If you actually mean the power light, that is supposed to blink when you plug it in and it is charging.

If you mean the one in the viewfinder, that is an error condition, and an error message is supposed to show up in the back image display viewer.
There may not be enough battery voltage left to display, so plug it into the AC adapter to be sure.

How old is the battery?

It's very possible that the blinking light is indicating a bad/old battery. These rechargeable batteries after so many cycles lose it's charging capability and the fault system built into the recharging base will indicate by giving you the red light on & off. Energizer rechargeable station is a good example when it detects old or bad batteries.

It is supposed to stay on. If it is blinking then your battery has gone completely dead. You can force the charger to charge the battery by applying a voltage (AA battery w/ wires worked for me) across the charging terminals while inserting the battery. You'll have to take the charger apart for this.

i bought some nimh rechargeable batteries a couple years ago and they still work to this day. im on my second camera with them and it does that to me when the batteries are dead. try opening the battery door when it does it and then close it and try turning it on again. if it does come on then its the batteries.

The camera may be trying to tell you that your flash is turned off in Auto mode, but to get a proper exposure you will need the flash turned on. Try turning the flash on and see if that works.

Hope this helps!

RED LIGHT FLASHING MEANS LOW BATTERY.

USE CRV3 LITHIUM OR NI-MH REHARGEABLE, TRY TO GET TWO IN A SLEEVE. SLEEVE REDUCES BATTERY MOVEMENT WHEN CLOSING LID, TO MAKE GOOD BATTERY CONNECTION CONTACT.

IMPROVE BATTERY LIFE:
ADJUST FLASH SO THAT IT DOESN'T ALWAYS GO ON, TURN OFF SCREEN WHEN TAKING PITCURES.

Make sure you look straight through the viewfinder. Keep in mind that the area visible through the viewfinder is slightly smaller than the area captured in the photo. If you're taking a close-up or macro mode picture, turn the camera dial to the LCD mode so that you can use your LCD screen to preview your picture.