Slipping transmission 2003 Jeep Grand Cherokee 2X2 6 cylinder. From stopped position, transmission slips when subjected to acceleration a bit above normal as in starting up a slope. What would be normal fee for adjustment.........transmission has been flushed but problem persists.

That is strange because they are unrelated.

The power steering works using a pump that has a pulley and is turned by the Serpentine belt. Where you put the fluid, did it look like this?

https://www.carparts.com/power-steering-pump/jeep/grand-cherokee/2003

https://www.google.com/search?q=2003+jeep+grand+cherokee+power+steering+pump

The Brake Master Cylinder has a similar reservoir and also has a brake booster that uses vacuum power from the engine to give you a mechanical advantage. Both are shown here

https://www.ebay.com/b/Brake-Master-Cylinders-Parts-for-Jeep-Grand-Cherokee-for-2003/33566/bn_87327012

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we cant drive car, so jerking is not clear to a non driver.
see>?
first off , ill guess there is no odd noises.
and that means jerking can be 2 things (sure more but)
engine jerks, does it only?
or transmission slips then stops slipping resulting in a jerk.

get it serviced, with persons that can drive and experience this live.

engine stalls.?
what cuts off, the radio:?

transmission slips (cuts has no real meanings, to vague)
stalls
misfires
bogs
slips
flares
shakes.
makes odd noise.
does car drive perfect in DRIVE (other shoe drops)

Jeep grand cheerkee.
what year.?
which of 3 engines> or more>?

my guess is revving , means, (its good word)
means, car dont move?
the transmission slips? (engine RPM rises fast , but car does not accelerate in the same proportions)
or the RPM fail to rise, that means the engine Lacks power
those 2 are polar opposites.
engine problem
transmission slip. (flare)
2 paths to walk. do not guess. or it gets expensive fast.

Test and check torque converter.

Sound like its in transmission.. Did you have sensors checked,could be the problem..

Did you ever get that problem diagnosed? My 2008 Jeep GC recently and frequently gets stuck and does not accelerate past 1st gear. We have to pull over put it into park then shift into D-rive again. Then the transmission accelerates prperly. The only way we knew this was the big trucks on my job site have to do the same thing. A temporary resolve. Hoping it's not the transmission slipping and needing repair.

you need to change the throttle position sensor. This is not a transmission slip so to speak but a flux in the throttle body. the part is easy to fix and on a V8 lies
right behind the resinator behind the throttle body. I had the same issue with my 02 GCL. Part costs 40 bucks

could be the filter was a bit bunged up ,as the brake bands and front clutch wear they leave fine particles which gets caught up in the filter

if fluid isn't burned, shifts aren't slipping or flairing and you did not find a large amount of debris in the pan, chances are that the electronic shift control is malfunctioning. Have someone check it out.