While your installation using the flex piece is not so good, if the only problem is the right sink not draining well, I would take apart the tailpiece on the right drain and the horizontal to the tee. See if there is an obstruction that you can remove.
Also clean out the tee.
To me it seem that cutting out the existing glued-in trap and putting a trap adapter near the wall, would give you the ability to adjust the trap position. That way you would not be resorting to a flex line.
But I do have hope that just cleaning will get you going. I am not a plumber.