My aim is to determine surface temperature extraction by computing NDVI from Landsat 7 and Landsat 8. suggest me which method DOS (dark object subtraction) or FLAASH atmospheric correction in ENVI will be suitable to compute NDVI?
If your goal is just to get the NDVI, i'd recommend you calculate it using surface reflectance product. One of the most widely used Landsat-based surface reflectance products is LEDAPS, whose info you can find here: http://landsat.usgs.gov/CDR_LSR.php. With this product, you don’t have to do the atmospheric correction yourself.
While I agree with the recommendation by @TonyC, it doesn't really answer the question.
DOS is not really an atmospheric correction, but a compensation instead. The base assumption of stable dark object is a risky one and it will not generally allow you to compare across different Landsat tiles. Contrast this to FLAASH, which is a decent atmospheric correction, and it should in theory be consistent across time and tiles.
As such, in general FLAASH beats DOS, but it also takes longer and is more of a black box when used. However, the Land Surface Reflectance products from USGS are generally good for most uses, which means that you don't have to do the atmospheric correction yourself, when using Landsat for most land applications.