I recently had crown prep work done for my two front teeth. A one piece temporary crown was put in place until the permanent crowns can be placed.

It has been one week and the gums cannot grow back together between the two fron teeth due to the temporary so I have a gum flap in the front and back. When the permanent crowns are in place will/can this be corrected so my gum heals back together?

I have no idea why your dentist would put your temporaries on as one piece. It certainly makes it difficult for the gums to stay healthy.
If the gums don't fix themselves your dentist will probably want to do a gingivectomy to make it look better.

Sometimes the temp will be splinted (one peice) for extra strength. The temp crown material we use will often break if the crown prep was conservative and it has to be thin to fit in between your bite. The tissue will likely come back with the permanent crowns, but MAY persist as a "black triangle" if the crowns are cut too deep, or are not shaped properly. Just keep the area clean and try to deal with it until you get the final crowns.