On another FL mod I saw (think it was Vanguard), the black holes attracted you towards them with their gravits.
So at least he gravity part or "gravity slingshotting" should be possilbe. Seems that gmae mechanics allow you to calculate an acceleration vector according to your distance from an obeject.
For the sail part to work, you would also have to take into account the orientation of the sail towards the sun. BUt if its possible, one matrix equation is enough to calculate the "sail" part accelration to your ship.
The difficulty I see is that for it to be half way physically realistic, you would have to have very very slow movement and accelration far from the sun. And that means... so slow that no one would ever want to fly that thing far form the sun.
And, the speed near the sun, for a realsitic slingshot to work and still be of ue for getting form a to b, would have to be fater than 420 I think.
To go around that, you could make a "sail deployed" mode for the ship, where it simply submits itslef to the forces of the sun, and a "sail retracted mode" where you could fly around like a slow normal ship.
another problem would be planet, since they have gravity too. Wouldnt be much harder to program than a single un environment, but would be very much more harder to try to fly a ship in a system where planets have gravity too.
All in all, I think its feasable for a single system as a fun sport, but not really possible to make a nice sailing ship that can make Siriuswide trips. And if you were to try that, you wuold have to program whole new physics into every system just for this ship. And would take a LOT of ballancing so that your sailing ship can get from jump to jump there.
Of course you can just put a big sial on a ship and imagine the rest. Wouldnt feel real tho.