P0300 on 07 G6

sounds like it is time for a complete tune up , check wires, distributor cap/ rotor arm/ timing ignition module/coil.
You seem to have no issue with supply of fuel perse but misfire is sometimes attributable to fuel / air mix problem

do the 60,000 mile tune up, yet
at the very least the new spark plugs?
or just get it serviced.?

I would go with new plugs and wires as a first fix after 223,000. I usually replace them around 100,000 miles.

P0303....Cylinder 3 Misfire Detected

P0304....Cylinder 4 Misfire Detected

sounds like a new set of HT leads and plugs wouldnt go amiss(fire wires) weird name that fire wires HT stands for high tension leads in proper english .

DID YOU GAP SPARK PLUGS AT 0.060 FOR 3.1L ENGINE OR 0.045 FOR THE 3.4L ENGINE.DID YOU BUY AC R44LTSM SPARK PLUGS. DID YOU BUY AC DELCO SPARK PLUG WIRES.BECAUSE IF YOU BUY WRONG TYPE SPARK PLUGS AND WIRES CAR WILL MISFIRE.

yes i would change the plug wires , you can take a spray bottal with water and spray that wire, and if it starts to run real bad then it is shorting out, you may also have a injector going bad you can test this buy puting a ohms meter on it and ck the ohms it should read the same or close to the same as the other if not it will need replaced

This is a very common problem....and can be a little difficult to troubleshoot.
How long since a tune up?
My 01 did this same thing at 80k miles..ended up being a bad coil. VERY easy to replace, so don't take it to a dealer unless you don't want to do minor wrench turning.
I first did an entire tune up with new plugs and wires....didn't help at all. I measured the resistance of the ignition coil assembly and found that #3 was reading lower than the rest even though it was "in spec". After replacing it, the van has run for thousands of trouble free miles! Worth every penny...gas mileage went from about 14 back to 19! Paid for itself very quickly.
The shocker in all of this was that after doing MUCH shopping around for a coil, the Dealer was the best price at around $80-90. Even Autozone and others were over that price....go figure.
IF you have not tuned it up in a while, pay the extra for a new set of plug wires and new OEM plugs and have them installed by someone competent. Getting the spark plugs installed at the rear of the 3.8 is not a whole lot of fun. I did it myself, but only because I enjoy working on my vehicles.
GOOD LUCK!

they say 30 to 50k. i myself prefer 30k especially in older engines. usually i check the plugs at 10k to make sure they look alright. you changed wires too right? newer engine can go 50k60k.

The flashing check engine light is typical of a misfire issue. There are two things I would do to start with.

1. Take the vehicle to an auto parts store like Autozone and have them hook up their scan tool so that they can retrieve stored trouble codes. Even if the check engine light is not on, they should be able to retrieve recently stored codes.

2. Do a complete tune up. New plugs, new plug wires, new air filter, new fuel filter if it has not been done recently.

If the parts store pulls the codes and they cannot tell you what they mean, post them up here and I will see what I can dig up for you.

Sounds like the distributor advance is sticking for some reason. Is it mechanical?