"Sun radiates 63.08 Million Watts/m2"
http://www.xomba.com/solar_constant_and_the_amount_of_energy_produced_by_the_sun

At Mercury distance the Sun radiates 9350 W/m2

The sun's escape velocity is around 600 km/sec or about
1/500th the speed of light.

And Sun orbital speed around the Milky way is about 220 km/s.

Wiki:
"An interstellar slingshot using the Sun is conceivable, involving for example an object coming from elsewhere in our galaxy and swinging past the Sun to boost its galactic travel. The energy and angular momentum would then come from the Sun's orbit around the Milky Way. The time scales involved for such an operation are considerably beyond current human capabilities, however."
http://en.wikipedia.org/wiki/Gravity_assist

So, from the perspective of someone outside our solar system, our sun is like any planet that can be used to gain energy by using a gravitational slingshot, assuming they are in the right time and place in order to get correct vector to some other star.
So, a space alien could enter our solar system at say 200 km/sec relative to the speed of the sun [and it's planets], as it goes towards the sun, it will gain velocity.
The 200 km/sec velocity, is 720,000 km/h, 17,280,000 km per day, and 6,307,200,000 km per year.
Neptune distance from the Sun is 4,495,100,000. And Pluto average distance about 5.8 billion km.

If an alien is entering the Sol system at the same inclination as all the planets of our system are at it's possible that he could use any of the planets to add additional velocity before using the Sun.

So, a question could be is any planet add any significant velocity, what alignment would planets need to be in to add the most from the planets and what direction would the alien have to enter and leave the solar system to get the maximum or near optimal added to velocity from a slingshot effect from this solar system.
Or are the planets insignificant in terms of how much an alien could get in terms of delta-v from the Sun.

If an alien knew or suspected how much velocity Earthling would have leaving the Earth/Moon system and where Earthlings might want to go: Mercury or Jupiter for instance. They could plot any possible trajectories, we would use for the next century. This finite number could fairly large depending upon the range of possible velocity leaving Earth/Moon
and the number of possible destinations and how much time we were willing to take to get to any destination.
Now, suppose an alien simply wanted to find a trajectory which earthling wanted to get maximum slingshot affect to send a probe to our nearest stars, here you would have a smaller finite number per Century. The number would depend upon how much delta-v Earthling would add to Earth escape velocity and when in the trajectory they would add this delta-v.

We could do the same sort of thing in regards the trajectories an alien would take- assuming
they didn't had such super duper technologies as warp drive that make any gravity assist unimportant.

Wiki said:"The time scales involved for such an operation are considerably beyond current human capabilities, however"
This isn't saying much. Suppose we had "starship" or "colony barge" which was in the range of 10,000 tons or more and we wanted to go to some star system fairly near us, and was willing to take a long time to get there. Would we use the Sun for a gravity assist and how would we do this? Is there a window for this in the next century, or what is best window in the next century.

Now, it seems to me that if Earthling were to do this, the trip to the other star system would "start" from a location at or beyond Jupiter's orbit and could involve Jupiter.

At Jupiter distance Solar escape Velocity is 13.6 km/s. Which also means that it something "fell" towards the Sun from Jupiter distance, it would approach 600 km/sec as it neared the Sun. Or that 13.6 km/s is about 2.25% of the Sun's escape velocity. Or if dropping from any distance from the Sun, at Jupiter distance you "get" about 97.75% of what is possible at furthest distances.

At earth distance solar escape Velocity is 42.1 km/s. Compared to the Jupiter as above, 42.1 km/s is about 7% of the Sun escape or 93% of what is possible at the furthest distance from the Sun. But to go towards the Sun, one needs to reduce one's orbital velocity around the Sun:
Earth: 29.8 km/sec
Jupiter: 13.1 km/sec

So, if you want to stop or reverse one's orbital velocity around the Sun [or change the inclination of orbit around the Sun, so involving Jupiter and Jupiter's distance from the Sun is a good "starting place".

At Mercury's distance solar escape velocity is 67.7 km/s.
Reference:
http://en.wikipedia.org/wiki/Escape_velocity

So continuing as above, but with Mercury; 67.7 km/s is about 11.2 % of the Sun escape
or 88.8 % what is possible at the furthest distance from the Sun.

So, if falling from Jupiter, one is only going to get a velocity less than 10% of Sun's escape
velocity [around 60 km/sec] and it would to take long time from a "dead drop" to get to those speeds- at Mars average distance solar escape velocity is 34.1 km/s [5.6% of Solar escape or 94.4 of what is possible], so velocity from dead drop from Jupiter distance by time you get to the Mars distance the velocity is about 19.2 km/sec.

So roughly speaking you whip around Jupiter, stop your solar orbital speed and charge towards the sun at something like 10 km/sec and by time you get to Mars distance you could traveling around 25 km/sec.
Distance between Mars and Jupiter orbital distance is:
JUPITER: 778.6 million km
MARS: 227.9 million km
So about 550 million km with rough average velocity of 15 km/sec at takes about 10198 hours. And a year is 8760 hours. So over one year. But thereafter getting to Earth distance is less than week and at the Sun less than one month.

So, most of your velocity will be added between Mercury and the Sun [88% of it]. The closer and longer you fall towards the Sun, the faster you go. On the way toward the Sun from Jupiter you could use the inner planets to add velocity/change of trajectory if they are in orbital positions that allow this.
And adding delta-v from rocket power when using gravity slingshots of the planets or the Sun will give you the biggest bang for your buck.

So, an obvious question is how can you get very close to the Sun which radiates 63.08 Million Watts/m2. It's not particularly easy to handle the extra solar radiation at Mercury distance [9350 W/m2]. The good news in this regard is that if you doing solar escape trajectory, you can't stay near the Sun for a very long period of time- you are simply traveling too fast. At 600 km per second you will go in some direction in one hour of time
2.16 million kms, so you simply can't be within one radius of the Sun for more than one hour- the duration nearest the Sun is a matter of hours not days or weeks.

So in terms of getting insanely close to the Sun in a solar escape trajectory, this could far easier than "staying in" 1/2 of Mercury's orbital distance or about 30 million km orbital distance around the Sun.
Or related to this, is that if you had a planet which had a highly elliptical orbit- more elliptical than Mercury, but got much closer to the Sun [say 25 million miles] and went the same distance furthest from the Sun as Mercury does, it's average planetary temperature could be less than Mercury or certainly less than a orbit which was circular
and was at it's average distance. Or Mercury's average temperature is less than "a Mercury" would be at Mercury average orbital distance [circular orbit].

So, to wrap this up. A question would be how meters of ice does 63.08 Million Watts/m2
melt in a certain time period. The "starship" could have say 10 meters thick of ice
which shades it from the Sun. And perhaps one could use the solar energy to heat up water for a boiler and use steam as a propellent.