Gas Dryer - Kenmore 80 series... - changed my solenoid coils and the flame still goes out after 10 seconds...

Hi Joe and welcome, before changing the coils did you check the other safeties with a meter? Have you checked the duct work to be sure it's clear?

Your dryer is most likely dirty and clogged up and you cannot tell this until you take it totally apart. Each load puts a lining of concrete-hard lint deposits on all surfaces. You will have to take it apart and test the thermal fuse near the burner. You will have to clean the drier out thoroughly or it is all for nothing. Every air duct will have to be removed and scraped and washed out to remove baked on lint deposits which is like a concrete lining. This will burn so the manufacturer has installed the safeties to keep from having a house fire. The safeties are oval-shaped with a round center part containing the safety with two plug-on terminals for the wires and when they burn open from the dryer being dirty nothing will work. Using an ohm meter you put a lead on each terminal of the safety with wires unplugged and if it's good you will have a reading of about zero; if it's bad it will read infinity. Driers were the number one cause of fires at one time, hence now we have safety fuses. Look at: http://www.youtube.com/watch?v=MMP7BW1lLs4 to see how. Also: http://www.youtube.com/watch?v=iBiRw-KElC4 ; http://www.youtube.com/watch?v=yFTZGgVisCI
Electric Clothes Dryers
Whirlpool Dryer Model LE5800XSW3 Wiring Diagram
When you finish cleaning the drier and install a new safety it is best to also replace the belt, too, because you do not want to have to disassemble it all over again and if the belt is over two years old you should replace it.

Note that on most of the videos it does not show them washing out the parts, but this is important because it's the only way to really get the parts clean, just don't get motor wet or the capacitor if it has one. Vacuum out the motor. I would move the drier out to your garage to have plenty of space to work. You also want to check your vent and clean it, also. The vent should have a short run and be straight as possible. The job is really easier than it sounds. There is no shortcut that will work; it has to be cleaned well. Before you re-assemble it make sure to use white lithium grease (high-temp grease) and grease all bearings. Just vacuuming out the dryer a little does little good.
Manuals: https://dl.dropboxusercontent.com/u/...l%20Dryers.zip
https://dl.dropboxusercontent.com/u/...e%20Manual.pdf
Just changing parts is good for nothing. You do not troubleshoot that way. I do not understand why people continue to do this in this day of cheap electronic meters. Attachment 47388
You can get this meter at Home Depot for $42.38 at: http://www.homedepot.com/p/Commercia...-205620397-_-N
Get a meter and study the manual I attached and you will never again make such an error.