Flashing check engine light and code P0304

P-0304 is a misfire code for cylinder number three. It can mean many things, from a bad spark plug, bad coil, bad fuel injector or even internal engine damage. The code is the ECM saying that cylinder number 4 isn't helping the vehicle so it's a problem.
The way to determine what the issue is would be by testing the various parts, the coil is the easiest thing to start with. The plastic covers on each side of the engine cover the coils. The number 4 coil is an easy one to get to. If you are standing in front of the car, remove the plastic cover and number 4 is the cylinder all the way to the passenger side/front of the engine. To test the coil and the lower parts you can do some parts moving. Disconnect all three coils and remove them paying attention to which is number 4 and 6. Next remove the spark plugs from cylinders 4 and 5. Look at number 4 and compare it to number 5, is there any obvious problem like wear or damage or what is known as carbon tracking on the plug or a white scorch area inside the coil boot.?
If so that could be the issue. If no obvious issue with the plug install the plug from number 4 into cylinder 5, then put the coils back on, swap the coil from number 4 with the one from number 6. That will give you cylinder 4 with the "good" plug from cylinder 5 and the good coil from cylinder 6. Then cylinder 5 will have the "bad" plug from cylinder 4 and the good coil it started with, and cylinder 6 now has the "bad" coil from cylinder 4 and the good plug it had.
Now erase the P0304 code and start the engine. It should still run bad if the bad part is still there but hopefully now it will not show a 304 code, instead if the plug was bad, it should show a P0305 as you moved the plug there, or a P0306 if the coil was the problem.
Then just replace the bad part, although if the plugs haven't been replaced in a while you may want to just buy a set and replace them in all cylinders as another one could be waiting to fail.
Now it is possible that you still have a P0304 only. In that case it could be the fuel injector or an internal engine problem. However run the tests above and return with what you found and if it's good news great, if not there are more steps to do to see if it's a worse problem.

Thank you Steve, your information was helpful and reassuring. I changed out all 6 plugs for NGK iridium's, and i had also switched the fourth cylinder coil with the fifth cylinder coil. While i was changing the spark plugs i went ahead and performed a compression test. The results showed all cylinders at 150psi to 153 psi. When test driving the car ran very well, and the CEL flashed as i had suspected it would, however when i pulled diagnostics this time around cylinder 5 had the misfire. New Coil is being ordered.

That is a technique called "swap-tronics" many times it works for testing without costing extra money to confirm a problem. Glad to hear it worked as intended. Compression is real good as well. I would say replacing the coil should take care of the as well.
Only other item I'd worry about is when the timing belt was last done, Honda doesn't list a mileage unless the vehicle is being operated in very high temperatures all the time, then they say every 60,000 miles or when the service indicator comes on for the belt. Personally I'd rather do it at most every 100,000 because I don't trust belts much.

A private shop had done the timing service at 86,000 the car is at 130,000 now. the car runs pretty strong currently so I'm hoping it will last at least until 170,000.

Sounds like a plan. Let us know if the coil cures it.