I have a American standard toilet # 98839 or 4266 made in year 07-12-09 I need a flush kit and a plastic vent that goes inside the toilet where the tank sits on top the bowl.

Your vent stack may be clogged. The pipe that goes up to the roof. Let's air into sewer pipes when you flush. A birds nest or something can do it.

There is a clog in the line. A plunger usually solves this problem, but you have to use a toilet plunger. Your local hardware store will give you the right tool ($13). If the plunger doesn't work, you need a toilet auger (also called a closet auger), which you can buy for less than $20.

I would suspect some sort of air lock in the pipe, or just a partial blockage which is slowing the water flow.
You may be able to clear it using a rubber plunger. You need a plunger that has a metal or hard plastic disk fitted above the rubber cup (to prevent the cup turning inside out).
If you have an ordinary plunger without the disk you could probably make one to fit it - perhaps the bottom cut out of a plastic drinks bottle and a hose clip to hold it in place.
You will need to work the plunger quite vigorously up and down in the toilet bowl to force a pulse of water through the system.
Pouring a large bucket full of water down the toilet after plunging may have more impact than just normal flushing. It will also refill the trap.

If you have that thing off, take it outside and put it up on saw horses, fill the back with water and flush it, see if it is still slow. Then get your kid to reach up there and get his toys out if it doesn't flush. You might have to do it a couple times. Then if it does flush, you know it is clogged down the line or something is blocking the vent. Got squirrels? Check it out.

I have worked on these for many years. The flapper that's attached to the chain and handle, sometimes drops to soon before the tank gets to fill up enough to flush completely. If the flapper has not been changed for some time, it would be a good time now. I wouldn't change out the toilet unless it is cracked. This is a well made one, and I would want to keep it.

your float is stuck

After working for ROTO-ROOTER for 20 + years, I have come across this problem more than twice. There are many problems that can be included, but let's start with the most simple and go from there. Step 1... Check your roof vent to see if it is obstructed with debris, such as birds nest, frozen ice, dead animal...etc..... To check this you must go onto the roof and find the sewer vent(it is not hard to find as it smells like sewer). Visually look into the vent even using a flashlight to make sure there is nothing obstructing the vent pipe. certain things can clog your vent such as Debris,Birbs Nest, Ice, dead animal,Etc..A drain line needs a air vent so water can flow....If nothing is visually seen , have someone flush the stool. If you cannot see any obstructions and HEAR THE FLUSH, Your Vent is okay. Check out plumbing and venting on the internet for more reference. If this is not your problem then you must pull the stool and see if there is an object stuck in the toilet......Comb, toothbrush, Etc... The best way is to pull the stool from the floor and look from the bottom of the toilet to see if there is an object stuck inside the stool.Turn off the water supply and disconnect it from the tank. Go to your local hardware store and buy 2 wax rings with plastic flanges and a set of flange bolts(these are cheap and can be returned if not used).Turn off the water supply to the toilet tank and flush it to drain all the water from the tank and the stool. You can use a shop vac or an old towel to remove the water. After removing the stool, lay it on its side and look from the bottom to see if there are any obstructions. You may need a mirror and flashlight to see inside the gooseneck of the stool. If you cannot see any obstructions, you can try to dump a 5 gallon bucket of water through the bottom of the stool to push the object out the way it entered. NOTE: When reinstalli8ng the stool, be careful not to over-tighten the floor flange bolts as you might crack the toilet......Joe

hello, this is a standard toilet you will need to inspect the flapper that is the rubber flap that holds the water up in the tank it works when you pull the lever it pulls the chain upward and lets the water flow if this flapper is old it may not stay up long enough for the water to flow. open the tank top and flush the toilet see if this flapper is staying up long enough and giving the tank enough time to empty if not change this rubber flapper its inexpensive part.
if this is not the reason then you need to adjust your water filler valve there should be a small screw on top of the pivoting float arm
if you have to adjust it for the water limit line inside the tank this will be the proper amount of water needed to flush once completely

also check that the chain lenth on the pull lever is not pulling the flapper down quicker than its supposed to,

try this let me know your results
hope it helps