I have a Schengen visa valid from 19/07/2016 to 10/08/2016. But the duration of stay is 7 days only.
I want to stay for 6 days more, for a total of 14 days. And my flight includes travel from a Schengen state to another.
You have a visa with a day count restriction of 7 days and you want to stay for 14 days.
The answer is yes, people do overstay their visas on occasion, there is not a border guard posted on every street corner checking documents.
The problem comes when you exit the zone and your documents are inspected. At that point your overstay will be discovered and you will be asked for an explanation. Giving a plausible explanation is virtually impossible because of the difficulty in providing representation, in your case it means some tenable evidence. So you'll be booked as an overstayer.
What this means is the possibility of of fine. Perhaps worse, it will be your final visit to the Schengen zone for a long time, on the order of a decade, so enjoy it. Alternatively, you can change your plans or apply for an extension.
The "best practices" advice is to ask the issuer to cancel your Schengen and issue one for a longer period. You would do that before you leave for Europe.
Schengen visa validity and days are not similar to US's style. In a Schengen single-entry 30-day validity, 7-day stay visa, you have a window of 7 days to stay in Schengen, a window which could start on thr first day of validity, and will close on the last day of validity.
For example, if you enter on the first day of validity, you still have only 7 days to stay. If you enter on the 24th day or after, you still need to come out on the 30th day or early.
It's either validity days, or dates, whichever gets used first. If you already used 7 days, the visa is consumed even if its validity date is still in future. If the visa is expired but you have not used all allowed days, visa is still consumed. Think of a smaller box (duration days) in a larger box (validity). You are free to place the smaller box where ever, but it needs to be inside the bigger box.
Flights between Schengen states are considered as local flights for visa purposes, and only the dates you enter and exit Schengen will be considered.