Can a married couple file separate consecutive chapter 7 bankruptcies?

It depends on how close together they are filed and the circumstances inolved. There is a chance the trustee will move to join the cases. You should speak with an experienced bankruptcy attorney in detail before considering this option.

The short answer is that yes they can (assuming they meet other requirements for filing a Chapter 7).

As my colleague correctly notes, they could be joined for administration if filed closely together in time.

My question is why do they want to file separately - with double filing fees, legal fees, etc.? If the court sees that the debtors are somehow trying to game the system, the court can take remedial action. I would be careful about doing this absent a valid reason that you would not mind discussing with the bankruptcy judge.