It sounds feasible but there are a few things you should check out. First, depending on the type of fireplace you want (wood burning masonry, gas with metal flue, etc.) the concrete floor you mention may have to be thicker and/or have footings under the fireplace. Second, the chimney has to extend a certain height above the adjacent roof (per local code) for safety reasons. Third, since it's a prefabricated gazebo, penetrating the roof could cause structural issues for the roof, unless the fireplace is situated so that it's outside the perimeter of the gazebo. Just some thoughts...

Sounds like a gazebo fire waiting to happen, especially if its a wood fireplace.