Hi Keshav,
It sounds like you are trying to integrate a Sencha library (ExtJS) and components as a Design Studio SDK component. Integration of external libraries is possible. I suggest you first review the Design Studio SDK Developers Guide which explains how to include external libraries.
As for the implementation of the Search Box, this will depend on what is available in the Sencha library. Again, I suggest you attempt this yourself first based on the Design Studio SDK Developers Guide documentation and then ask more specific questions if you run into difficulties.
Regards,
Mustafa.