Minimum drain pipe (less than 3” in diameter) slope requirement is ¼” per linear foot, which gives you 7.5” on that 30’ run (IRC - International Residential Code and UPC – Universal Plumbing Code). If the drain pipe has a 3” or larger diameter IRC permits 1/8” slope per foot (different jurisdictions adopt different codes) / UPC doesn’t.
Those are the minimums but to increase the flow you can pitch the drain pipe slightly more, if you have room of course.
Some other requirements you need to keep in mind are:
Drain pipe size which will depend on number of kitchen fixtures and your local code. For example; just a sink would require 1 ½” diameter p-trap and drain pipe in IRC and UPC, however, kitchen sink with disposer would require 1 ½” trap and drain pipe in IRC / 1 ½” trap and 2” drain pipe in UPC.
Drain pipe support (depends on material used); i.e. ABS, PVC DWV – every 4’ horizontal IRC and UPC, in UPC additional support at each horizontal branch connection, copper; every 10’ for 1 ½” or larger diameter in IRC, UPC is every 6’ for 1 1/2” or less and every 10’ for 2” diameter or more.
Support is extremely important to avoid sagging of the drain pipe which might result in waste accumulation and clogging.
There's also plumbing vent issue but I'd have to know the configuration of your plumbing system.
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