When I accelerate my car starts to chug and the check engine light starts flashing.
A flashing check engine light means pull over and shut off the engine. Continuing to drive this car may cause damage. I’d have it towed to a Volvo dealer or mechanic.
A flashing Check Engine Light (CEL) indicates that the engine is misfiring.
If you allow that to continue unchecked, it will result in damage to the very expensive catalytic converter and may also damage other parts. You need to drive the car directly to a qualified mechanic (NOT to a place like Midas, Meineke, Monro, Sears, AAMCO, or any other chain operation) to have the problem diagnosed and fixed.
By contrast, a steadily-illuminated CEL can be dealt with when it is convenient, and in most cases the car can be safely driven with the steadily-illuminated CEL. Unfortunately, with the flashing CEL you do not have the luxury of waiting unless you want to risk increasing the repair bill.
What about the chugging??
As VDCdriver said, it’s misfiring. The misfire is the reason the CEL is flashing. You should not drive it this way.