Craftsman 19.5 lawn tractor w/briggs & stratton keeps flooding

This could be a number or items from no spark to a faulty carburetor, a plugged up air filter, valves out of adjustment, poor gas, faulty spark plug.

First, see if your getting spark, how about taking the wire off a plug(s) and holding it about 1/8" or so away from the plug with some masking tape while you crank the engine. You should be able to see the spark jumping the gap, it helps if it is not too light outside. If you attempt to do this with your hands, you will get a spark jolt, it hurts, so use the tape and remember, the engine could start so proceed with caution.
If you have no spark there, then you ignition or magneto is faulty. This would be unlikely in the broader scope of things. You will likely get spark. Make sure the plug is clean, take it out and inspect. If it is covered in gunk well clean it. It will smell like raw gas but you already know that. Change the plug if in doubt.

Remove and clean and replace the air filter.

If you have spark, and a clean filter it is likely a carburetor problem, Depending on the carb, it could be the choke is faulty or, as per the below.

Depending on what model you have there is a float assembly in the carburetor that stops the fuel from flooding the carb and air intake. The gas tank is higher then the carb right, so if you dont have a mechanism for stopping the fuel from leaking out the hole that goes into the engine, it will all leak out right, as into the fresh air intake because its easier than going into the engine. So, there is a miniature float assembly, sort of like your bathroom toilet float to stop the water. Well there is a small wedge type needle that seats into a hole and it is attached to a float. As the gas rises in the bowl, it pushes up the float, sealing the gas into a chamber, as you use more gas, the float lowers and more gas goes in. So ,there is dirt jammed into the float bowl sealing needle, just a little, thats all it takes. So, shut off the gas somehow, hopefully you have a valve, or squeeze the rubber line, then undo the float chamber, its one nut on the bottom. Clean carefully. The needle, little spring and float assembly are delicate. Also, the needle could be worn from engine vibration, so it may need a new needle. It would help if you described the engine and carb though.

I posted that as a solution to another problem, but yours may also be the valves need adjusting. Depending on the amount of hours, say over 200, then the valves timing will likely be off a bit. Check the clearances with a feeler gauge, it is not as difficult as it seems. Check your Owners manual for the clearance at top dead center. TDC is when you take the plug out and watch the piston arrive at the top of the cylinder through the spark plug hole when you are turning the engine over (do this by hand, battery off. Make the adjustments with the valve cover off. Follow the instructions.

Hope some of this helps.

First, look to see if there's oil in your gas by smelling it. Feel the viscosity and notice thin it seems? You have a few options to check: first and foremost, look on the side facing out on the carburetor. Notice if the welch plug is still in place. A welch plug is simply a concave shaped circle made of aluminum. It seats loosely in it's seat built on the side of the carb. You can replace them yourself. Here's how: get a flat faced punch approximately 1/4" or 3/8" in diameter. Position the plug in place and using thd punch to hold the plug in place, center the punch on the welch plug and with a sm/med ball peen hammer, give it a couple raps. No more than two and remember they are aluminum and are soft.
Next, it could be the float stuck in the carburetor. If you pay attention to detail, they are simple to remove and rebuild (R&R). Youmust drain the bowlof the carb using a 1/2".wrench. if you have a shut-off solenoid, you need a thin wrench. Same size. Drain fuel in clean pan and let the fuel run into it for inspection. You can guesstimate what shape the carb is in by the way she smells and whats in the bowl. Oxidatiin, varnishing from old stale gas. Gently reach up and lift the float up with your finger, Do rnot force it.if it travels up and locks up, or if you raise and lower the float gently with your finger . Notice if the fuel metering jet sticks when you let the float back down. Orrrrr,
it could be a throttle butterfly in the carb. There are actually 2. One may have come aloose. There are screws pre-dipped in Loc-Tite to secure the butterflies in their respective places.. hope I could help