Is latex paint harmful to kitchen sink?

To the sink itself? Not if you don't mind it getting painted... temporarily. Most kitchen sinks are metal, enamel, or porcelain, none of which latex paint adheres to particularly well, so you can most likely peel the paint off fairly easily even after it dries.

To the Plumbing? It could theoretially clog the plumbing, but you'd have to pour in quite a bit and let it sit until it hardened.