Question

Will my tire go flat without the valve cap?

No. Your tire won't go flat without the valve cap.

It is a common misconception that you will lose air without the valve cap. So, the air in the tire is not affected when the tire cap is missing. However, the valve is necessary to keep the moisture and dirt in check.  

So, when the tire cap is missing, there is no possibility for your tire to go flat, but the chances of dirt entering your tire increase. Therefore, to maintain your tire in good shape, it is better to replace the valve cap as soon as you find it missing. Tire caps are cheap and can be found either online or in an auto parts store.