After selecting client as Firefox and checking delete and clear cookies option and clicking on "Ok" button , it asks to close all browsers instance but after that it does not launches anything
First make sure that you do not have any other Firefox instances running in the background and try again.
If you open the NeoLoad log files through the menu "Help-->Open logs folder..." and check the "neoload***.log" files. Do you have any error related to Firefox?
If you already have a recorded a request in your project then go to the advanced panel of that request and then select the recorded response tab. You have a "Open in browser" button. Does it open Firefox?
Otherwise as workaround you can still manually start Firefox and change the proxy settings to "localhost:8090" and then start a NeoLoad recording without starting the browser. It will allow you to record your script.