Depending on the way the track curves after the turnouts, it might be better to use a curved turnout. This is a single turnout, but both its routes are curved. Walthers sells them, and so does Peco. Or, if you have a unique situation where no commercial offerings will be suitable, have one made. What you need to do is to mock up the rails with flex track over graph paper. Then, with it all pinned into place, take a pencil and make a rough outline of all the ties, and mark where the tracks cross. That will be your frog. Either craft the turnout yourself or have someone make it for you. There are people in the hobby who build hand-laid turnouts for unique geometries. Won't be cheap, but you'll get precisely what you want.
If you can make it so that the twin tracks are parallel for about 6" before the turnout starts, and so that the exit at the points end extends tangent at least 6 inches, a simple Wye turnout (the two exits symmetrically exit at diverging angles, even curved if you need them to) will do.