If you check out the documentation for the streamline function, you'll see that you can specify the maximum number of vertices the streamline will have (i.e. how long each streamline is).
By changing the last line of your code to this:
streamline(X,Y,u+u2,v+v2,startx,starty,[0.1,20000])
where 0.1 is the step size (default) and 20,000 is the max number of vertices, the plot looks like this:
