I have applied for 6 months visitor visa and as the intended duration, I've given 2nd Aug - 14th August. My visa should be valid upto January. So can I extend my stay to 20th August after I get my visa (while booking my flights)?
You have a six-month Standard Visitor Visa expiring in January 2017. At the application stage you told them you wanted to visit for two weeks in August and you want to change it to three weeks in August.
That's fine. This does not result in an overstay because you're inside of the visa's start and end dates.
The only consideration is that you signed an agreement during the application stage where you agreed to notify them of significant changes. All other things being equal, going from a two-week visit to a three-week visit during the high season doesn't meet the reporting threshold; in other words, you're good to go.
You will still have a landing interview when you arrive so be sure to bring a return air ticket and your accommodation paperwork.