Try two cups of glass cleaner with an extra shot of household ammonia and a tsp. of dish detergent (very effective grease cutter). You'll need rubber gloves, plastic bowls and several old dishrags and towels.
Fill a small bowl with the solution. Close the blinds in one direction and swish down and across the entire surface with the brush, wiping down with a clean, damp dishrag. Rinse in sink, wring and replace dishrags as needed. Close in the other direction and do the same. Dry each slat individually with a clean cloth or use a hand held hair drier.
Repeat if need be until your kitchen blinds sparkle or whatever it is they do when they're happy 