I can't see that it would be an issue being on a Flat surface,In the past i used to do all my cars on a level surface but that's a luxury i don't have anymore as my driveway slopes and anything involving jacking the car up means a lot of wheel chocking
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Main reason the Punto is such a PITA to bleed air is that the Radiator hose bleed screw is a lot higher than the Coolant reservoir as there is no header tank as such.
So basically you end up trying to fight against gravity in order to get the coolant level higher up in the system than the coolant reservoir level sits at.
Only advantage really from having the car facing uphill was it made the Bleed screw lower down and the Reservoir higher by a few inches compared to being on a level surface, my Drive is about a 30 degree angle.
But Forcing coolant through the system with a bottle should work equally well on a flat surface, best suggestion is try it and see if it works OK
I also found that when you upend the bottle onto the coolant reservoir it helps to push it down a little creating a seal when you squeeze it, also the bottle effectively increases the Height of the coolant level in the tank to a similar level to the bleed screw and kind of acts like a header tank.
I know some people try running the engine to get the water pump to force the coolant in and the air out, i tried that BUT main issue is the engine warms up pretty quick and then you end up Going Ouch trying to put bleed screws in when there is hot water coming out.
I did the fill using the bottle with everything cold and only ran the car after i had bled all the air out. Once everything had cooled down again i forced more coolant in with the radiator bleed screw out to see if there was any more air in the system (there wasn't).
Also been keeping an eye on the coolant level last couple of days since i did the job and levels haven't changed.
I would also suggest that if your'e doing the job on your own then it helps to remove the air filter as you can access the bleed screw more easily, and you can also reach the bottle to squeeze at the same time.
Initially I put the bleed screw in hand tight to seal it, then tweaked it with a screwdriver , radiator bleed screw in mine i just hand tightened,seems to be perfectly adequate as if i remove the filler cap of the reservoir after the Engine has been running it makes a hiss , which shows system is pressurizing ok.