iPhone 5c Charging Port Issues

My problem is when I plug my iPhone 5c to charge/sync, the battery icon flickers on and off as well as the connection to the device.

I currently can't find a fix for this issue and I'm hoping I can get this fix. It's not a faulty cord because I tried multiple lightning cables and even cleaned the charging port, and the problem still persists. I really don't want to buy another iPhone just to fix this issue and since I've had the same phone for over at least three years, I'm pretty sure the warranty is no longer in effect.