Running water through the drain, assuming the drain will flow at all, should suffice to carry away most of the residue of the earlier attempt.
I generally don't recommend using drain chemicals. For the price of two big bottles of that junk, you could have bought a drain snake. Use the drain snake once and you're done. You don't wonder whether the drain is clear because often you pull up a big wad of hair and soap scum and boom, there it is. You KNOW the drain is clear.
Seriously. Next time save your money. Buy the tool that actually fixes the problem. It'll fix it better and the drain will work better, longer and unlike the chemicals, when you use it and get the drain cleared and the job is done, you still have the tool.
Hi, and thanks for responding. It's good to get feedback once in a while. Too often advice given on Y!A seems to go into a black hole and you never know what came of it.
Get the drain snake anyway. Drain chemicals don't work great on food in my experience, but the drain snake will chew right through it, snag anything big enough to actually be stuck in the pipe and drag it out, etc.
Take note whether your kitchen sink has a disposal. If it does, that may be the source of your problem. People tend to treat them as a black hole of another sort, a gizzard into which you can throw anything, flip the switch and problems simply disappear. Let me tell you - it ain't so! It chews stuff into smaller bits, sometimes macerating food into a mighty fine glue. I could tell you about LOTS of rice jams because people though the disposal would "get rid of it." No. Traditional Japanese shoji (portable folding screens, you know the ones) are made with the paper panels held in place with rice glue, and I really enjoyed watching the carpenter make the rice glue with rice from his lunch. HIS LUNCH. Scoop a little rice out, add a bit of water, mash it up: glue.
Sound familiar? Like a disposal?
Anyway. A drain auger from the hardware store can be had for about $25, not too bad. You may need a large slip joint pliers (tell the person in the plumbing aisle what you're doing, they should be able to point you to the right tools easily) to undo the drain connecting nuts, and you'll want a bucket.
The whole tool list for a typical kitchen drain clog:
Slip joint pliers about 10-11"
Rubber gloves (trust me on this, unless you're just not squeamish at all)
You want the bucket under the joints when you loosen them. It'll save on mess.
Turn off power to the disposal before you mess with it. I turn off the box AND pull its fuses before I mess with ours, but it's a big commercial unit (7-1/2 horspower) that can literally eat your arm, so it's a little scary.
Undo a couple of joints so you can get a section loose, and run the snake up toward the sink. Turn and push. Keep at it until you know you're right up against the bottom of the sink. Do it again toward the disposal if yours is a two-bowl sink. Then send the snake through the U-bends and as far down the pipe as it will go. Turn and push. If you run into resistance, it may be a turn, it may be a blockage. Keep the pressure on, keep applying torque. If you need to back up a bit and advance again, do that. It's food, it went through the drain grates at the sink or chewed to shreds by the disposal, so it won't be very tough whatever it is.
When the drain is cleared, put everything back together and run plenty of water down the drain. Watch it to make sure it doesn't start backing up again. Sometimes I put the stopper in the sink and fill it up, then let the full sink drain to push a big slug of water down and clear things out thoroughly.
When you're done, shoot plenty of WD-40 into the auger's can to keep it from rusting. It can go with the pliers into the bucket and gloves, ready for the next time. Having this small collection of tools can virtually eliminate ever calling a plumber or drain rooter for a clogged pipe. It will eliminate you EVER needing to waste money on barely-effective drain chemicals, ever again. Every time you use it, the original cost of the tools ($50 or less, generally) is amortized over all the uses, and the drain clearing expense becomes cheaper and cheaper per instance. It costs more today but is cheaper every time after that, for as long as you continue to do it this way.
Good luck with it.