As always: This is, how I did it. I am not to be held responsible, if my ideas cause any damage or harm...

First: Which pwr. steering Fluid? Thanks for asdf and Don for confirming what I thought should be the right fluid:
I checked the internet: Dexron III
I checked the part of the owner's manual called "Vehicle care" page 19: "Top up with Dexron III".
And it looks like that most Multi-vehicle ATFs (Automatic transmission fluid), who "claim" to be suitable ilo. Dexron III can be used.
I have plenty of that, because I wanted to use it as ATF, only to find out that you just cannot trust the claims of multi-vehicle ATFs reg. their suitability. I chose to pay more to get the correct ATFs. Thus, that multi vehicle ATF was now spare.

The required amount of that pwr steering fluid is about 1L, but I used more.

I tried to find a guide anywhere on the internet for the X308, of how to do all this. Could not find anything. But I knew, how it works on other cars/models, This here was a lot more difficult, because I had to remove and turn the reservoir (to get to the return hose to remove it). I am sure there are other methods to do the flush, but that is the method I chose.

The full flush:

Let's start with an "art-picture"... You can see what is important: I use heat-glue to glue a bit of tube onto a syringe to empty the pwr. steering reservoir bit by bit and fill the waste bottle with the old fluid. PS: Most of all I am feeding the little tube on the syringe past the "upper platform" (bypassing it on the SIDE of the iner platform) to get lots more old fluid out.


Then I detached the reservoir from its bracket. Also, I have to determine, which of the two hoses the return hose is. You can see it, when you look into the reservoir. On the Ford Fairlane NL and the S-Type the return hose is the upper hose, but this here is the other design as used on the X-Type: The lower hose connects to the pipe, which rises up INSIDE of the reservoir so that the lower hose effectively becomes the "upper" hose, if you know what I mean.


Next I lowered the reservoir so that I can empty it even more.


Then I removed the brackets of the reservoir entirely (careful not to loose parts: There are tiny metal tubes inside of all 3 rubber buffers), pushed the clips of the hosed back and used pliers to free the hoses so that they can "twist-turn" around the point where they are attached. The lid of the reservoir is back on!


It proved to be extremely difficult to get the return hose (the lower hose) off. Afterwards, getting the hose back on was equally difficult, so I resorted to using a heat gun, to warm up the rubber hose a bit, which was very helpful - I should have done that already at this point here, during the removal.


I stuffed on end of a bit of tube with heat-glue and put that tube over the reservoir's return-hose connection to close it off temporarily.


I stuffed a suitable hose into the return hose (and fixed it with that metal clip). The reservoir rests here on a brick. I filled the reservoir with DEX III. That is already the utterly black & dirty old fluid in the tube. It is there already, because I very briefly started the engine to confirm that I had indeed the return hose...


That hose extends to the waste bottle. You need a helper now, who starts the car (in P position and handbrake on) and turn the steering wheel to both sides on your command, and advise your helper to stop turning the steering wheels and turn off the engine immediately when you shout STOP. Meanwhile you stand prepared with an open 1 or 1.5 Liter bottle of Dex III. I used a milk-bottle filled from the 20L bucket in preparation. Things will happen extremely fast. Make sure that the hose is secured and cannot fly around spraying the ATF all over the place. Because it will - if it can - fly around like a open water-hose in the garden, after you open the tap. The reservoir will empty in a heartbeat, you have to poor the ATF very quickly into the reservoir, if you are too slow, you will hear the pwr steering pump squeaking. It's about 5-10 seconds until you have to shout STOP.


The old fluid in there was unbelievably dirty (black, right). That was the result from the action above. After those hectic 5-10 seconds, I refilled the reservoir, and I asked my helper to briefly start the engine only (no steering wheel action this time) until I shout STOP. Took about 3 seconds. What came out, was already the new fluid - the fluid in the left bottle above... PS: These are 1.5L bottles, i.e. (as you can see) I used just under 2L Dex III, as I had plenty of that fluid, and because everything went so fast at the first round of the flush that I could not shout STOP fast enough (I had to fill in Dex III first anyway, and I was just baffled of how fast the reservoir was empty.

Put everything back together. After attaching its lid again, turn the reservoir over again, remove the "plug" and put the return hose back on, turn the reservoir back into its correct orientation and then move the clips over the hoses (to secure then - now they also cannot turn anymore). Reservoir back into mounted bracket. Check fluid level.

I did all that WITHOUT doing any spillage.

 

And remember that there is still old oil in the steering rack if steering wheel is not moved. Valvebody in the rack just sends the oil back to the tank. There is not much oil in the rack. But when the total amount is small the % is high.

 

No spillage is impressive mate, good job!

If you don't have a helper, you can siphon out the old stuff from the reservoir and put new atf in. Start the car, turn the wheel back and forth. Repeat this 3 to 4 times to get newish looking fluid. Total, it takes about 1.5 to 2 quarts of Dexron III spec fluid. It won't be as thorough (more akin to a fluid change instead of a flush) it will get you out of a pinch.