I am extending our existing hardwood floor through the kitchen and bedroom. I bought Adams oak prefinished, 3/4" x 2-3/4". My plan is to weave it into the existing floor which was just stapled onto the 3/4" plywood subfloor and has quite a few gaps between the boards. The local building supply where I bought the new flooring said I should put some glue on the tongues when I install the new floor as well as nail it down over 15# felt. I haven't heard of glueing the tongues and nailing, but it sounds like a good way to keep the boards from separating. Is there any reason I should not install the new flooring this way?

They must be referring to the tongues on the old flooring that you are weaving into. I don't think that is a good idea aside from that.