1996 ford Taurus is cold?

I've had my thermostat changed and I've had it flushed. The 1 st time it was flushed it began to warm up only when you stepped on the gas. Now it's too the point it won't warm up when you step on it. I have no leaks and the car does defrost but it's cold air. Is this my heater core gone bad and is it expensive to have changed?

Find another one and use it for parts.

If the engine isn't overheating and you have no leaks as you said, the most likely causes are either a stuck heater control valve or a clogged heater core. If its the valve its easily replaced, if its the core and you've had the system flushed, it will mean a replacement. Heater core replacements are notoriously labor intensive since most require removal of at least some sections of the dash.