Well, I'm a idiot. And need help with a simple repair. Please

Stupid story short, I have a 2007 Chevy Avalanche. i am also proud owner of a portable Kobalt AIr Compressor. Well, first time, I learned that you need a cool-down period. At around 10 minutes in, I saw smoke coming from the plug. Second time friend needed to use it and lost track of time. Burnt it out again.No more front ones. so the other day I needed that charger again. so i plugged it in, in the backseat outlet. Used it but forgot to unplug it. third one burnt.

How can I fix those 3?

First welcome to the site,
Not sure what model compressor you are talking about, is this like yours:
http://www.lowes.com/pd_146781-40883-KL12120_0__?k_clickID=4ce570fc-c205-4b98-8ed0-ac91881837c4&store_code=86&productId=3522750&selectedLocalStoreBeanArray=[com.lowes.commerce.storelocator.beans.LocatorStoreBean%402cfb2cfb]&storeNumber=0086&kpid=3522750&cm_mmc=SCE_PLA-_-ToolsAndHardware-_-CompressorsDiyAndStationary-_-3522750%3AKobalt&DM_PersistentCookieCreated=true&CAWELAID=&CAWELAID=1071029347#img

Also what are you having to pump up all the time that it has to run for over 10 minutes at a time?
I am not an electrical guru but it sounds like you are overpowering the plug circuits. Since they were smoking you need to replace fuses and check sockets for burning and damage, may need to replace the sockets as well. You may want to consider making up a heavy duty wire setup directly from battery to a heavy duty plug so it can handle the usage. I don't know about their use but you might look into a power converter that changes 12volt to 110 and use the compressor in 110 mode too? I guess you could consider carrying a tank or two of compressed air so cut down on compressor usage too?
You may also want to consider getting a second battery as a deep cycle battery so you don't deplete your starting battery and get stranded somewhere.
Good luck and maybe one of the site experts will chime in soon.

I have to ask what are you inflating also. The dual batteries are a good idea, some of us have installed air compressors and a air tank for our train horns.

If plug melted then it had bad connection inside and you will need to replace as it could have melted.

What should have happened sithe fues should have POPPED to prevent this potential FIRE.

I am SUre GM has a PN for the outlets.

Cut the 12v adapter off of the compressor and add alligator clips so you connect straight to the battery.