You need to define the issue by isolating the problem. IÂm going to say, that the person who came out was not a plumber. He may have some other credentials, but not a plumber.

To isolate the problem, let me ask you this: is the rest of your plumbing OK? Do the toilets flush away; and the laundry drain away? Is this something entirely about the kitchen sink?

Then, it isnÂt out in the yard, $1400-worth. You need more information.

And we can help.

Pinoke

mechanical failure could be identified by means of videotaping the line. This method is less expensive and less intrusive.
And as pinoke said, since the sink does drain there is no failure at least of your main.
There is likely a problem with piping for the sink. A good guess might be grease buildup, but cant say for sure. I would definitelly get a second opinion from a reputable plumber...a tip might be looking in the yellow pages for someone who puts their license number right in the ad DO NOT CALL A DRAIN CLEANING SERVICE.