I am kind of confused. Is this the right way to go about this?

I am laying 3/4 inch x 3.25 flooring (continuous) in two rooms and a hallway and will have to start in the middle portion and reverse directions to accommodate walls. What I plan to do is cut a spline out of oak and glue it into the groove. I was going to make this spline fit fairly tight and glue it and clamp it letting it dry.

I was then going to screw down 6” wide ¾ inch plywood where the first row would start. The plywood would have a grove cut in it to accommodate the starter strip I just made with two tongues. I would nail it against the plywood using 2” L shaped cleats in the factory tongue and continue on with a couple more rows.

Now here is the question. After I remove the plywood starter strip do I go back and nail down the glued in tongue? That would make one board nailed on both edges. I don’t want 6” of board not fastened down (flexing squeaks) but on the other hand will a board nailed on both edges not be able to move and crack?

You should only need to make the spline thick enough so that it doesn't fall out if you were to insert it into the groove and then tip the piece of flooring so that the inserted spline is hanging downward. I've done my splines after the flooring is on the sub-floor. If you do it your way just be sure that the spline is at the correct angle...if it's tipping upward or downward then you will have trouble when you install the next piece of flooring against it. I have the piece already on the sub-floor, put glue in it's groove and on the spline (careful not to get glue on the floor surface), put a couple of scrap pieces of flooring against the piece that has the spline so that the spline is in the grooves of the scrap pieces....this will keep the spline at the correct angle. I nail the spline at this point.....some let the glue dry first....I figure the spline is not going anywhere so why wait. I nail a floor board's tongue and spline.

Forgot to add this to my previous reply but I think you're going to too much effort putting a groove in a piece of plywood. Just screw a straight board to the sub-floor along the center line and butt a piece of flooring to this board (groove side of flooring against the screwed down board) and nail though the tongue. Continue installing a few more rows of flooring in this direction. Then remove the screwed down board and install the spline as previously described and you can now install flooring in both directions.