Look. Let's back up & try to unconfuse things a bit. The problem is the OP has done a hydraulic oil and filter change and now his hydraulic pump is not moving fluid. So in his original question in the title of this thread the he asks,
"Can the hydraulic system get air locked after a fluid change"
The answer is that in an open center hydraulic system like his Kioti and most small tractors use, the hydraulic system cannot get air locked because it is not a sealed system. The sump is always open to the atmosphere by way of the vented sump. Hydraulic fluid cannot get "air locked" because one end of the circulation is open to the atmosphere. Any air gets moved along - or not - to the sump and escapes to the atmosphere. That's not to say that there can't be trapped air in the system causing other effects, but it won't cause an "air lock".
An "Air Lock" is not why his pump isn't working.
BTW, the radiator and cooling system are different.
Modern tractor cooling systems ARE SEALED SYSTEMs. They are not open to the atmosphere unless the system overheats. They definitely do have to be purged of air during filling because once the radiator cap is tightened down that system is sealed. It is not open to the atmosphere, so with the radiator cap in place there is no way for air to escape. In a sealed cooling system a trapped air pocket doesn't always mean the entire flow is blocked, but it can be. It will create a "hot spot". So there definitely are ways that an air lock can cause heating problems in a sealed system.
Hope this helps,
rScotty
Air can be still trapped in an open system Scotty.
Although less likely than in a closed system.
Customers like to save money and do fluid change service themselves and who can blame them. Not to accuse the op of improper procedure as I have no proof of that either way, We have experienced in these situations where the customer has started their tractor being minus the proper amount of fluid with the idea they would get more fluid later on or worse, where the customer, after a few quarts thought they had to start their tractor thinking to get the fluid moving.
The insufficient amount of fluid can cause tiny air bubbles or entrained air and keep coming because of turbulence. Another cause would be tiny leaks in the system constantly drawing in air such as a misaligned filter gasket. Yet another would be high points in the hydraulic system creating dead air pockets.
Ordinarily, this air as you describe in an open system, can be jettisoned with merely a few turns of the steering wheel saying everything else is tight.
If this pump has failed, no amount of coaxing will get the air out.
If it were me, Id start all over again. 1. Drain and save the replacement fluid. 2.Undo the filters making sure of proper gasket integrity and alignment then re-assemble filters.
3. Check all hydraulic unions to make sure of tightness.
After thats been done, refill the tractor to proper level being careful not to get any splashing that the glug-glug coming from the fluid can will cause. This can place unwanted air into the system. Refill with the spout at the top and a funnel sticking out of the fill hole to mitigate this. The first thing to do is to move the steering wheel back and forth after start up. It would be a good idea if the filters were preloaded with a bit of fluid even though most of these on smaller tractors are horizontally placed.
I know this is rather a pain but it will be a telltale if the pump has indeed failed. If not, then it's a cheaper and a simpler fix even having to repeat the fluid change procedure rather than springing for a new pump.
Hopefully the op's pump is still intact.