skip the middle...BUT if you do use it..wash it well first...

Most of the time there is no batting needed for flannel quilts. Since you want a light summer baby quilt, I wouldn't put anything between top and flannel back.

I make a baby quilt for each great niece/nephew that is born. The top is pieced flannel and the back is a minke type fabric. It has plenty of body already but I do use white quilting fabric as the batting. The reason I do this is because I think that the flannel and minke both stretch and if I didn't put that stabilizing fabric in the sandwich, the quilting stitches would tend to break from the stretching. Just a thought for you. Although, you did say your top was normal fabrics so your situation is not quite the same as mine. Good Luck!

BTW - I prewash all fabrics in hot water and dry in a hot dryer. I assume parents will want to use these temps when washing the quilt so I want to be sure there are no bleeding or shrinking issues.

I would put a very thin batting inside. Something like Thermore. With air conditioning I don't believe this would be too hot and will define the quilting. However, before you sandwich, I would put the three layers together and feel and see how heavy or hot they may be.