Still,

So, you know the blockage is more than 20 feet down-line from kitchen sink.

Look for cleanout caps just outside the house on the line leading tot he city sewer. On later homes they are round black ABS plastic with square heads for wrenches to start unscrewing them. Older homes have cast iron ones.

This will let you access the line further down and snake back up -- if you can -- and down from there.

I've never used a hose for this purpose.

A