Can a Verizon Iphone 4s somehow be converted to be used on the Sprint network?

If not, how can I flash my phone to different company?

Yes it can. Just cancel your data plan and bring your phone into the new store and they should be able to do it for you.

You can get the Verizon iPhone 4S flashed to Sprint and use it on Sprint. You can mail this person (arghyle@rocketmail.com) who can help you get the phone flashed.