You need inline flue damper as the change to double will absolutely increase the draft as pointed out above.
I guess my personal home energy goal is along the lines of not having drafts in my house by having a house that is sealed well enough not to leak much air by itself. The house stays warmer in the winter and cooler in the summer using less energy year in and year out. A tightly sealed house then creates the need for combustion air, and I personally prefer to have it piped to the stove or next to it to avoid the cold drafts through the house that make me feel colder than the thermostat suggests. I can say that with each step to controlling air leaks in this house, it has gotten more and more comfortable because there aren't cold drafts any longer. We are now at the point when we do need an energy recovery ventilator to get more fresh air in the house.
All the best,
Peter