when i use the jar that i found in my project's build/libs folder to test its working on common mc launcher(not inside intellij) and i got this:
Caused by: java.lang.ClassNotFoundException: kotlin.jvm.internal.Intrinsics
i used kotlin in my project, but the main entry class is in java and i added fabric-language-kotlin in build.gradle's dependencies

how can i install it?

You just need to download the FLK jar and put in it mods like any other mod.

Have you also installed FLK in the mc launcher mods directory? It needs to be there as well. (And preferably in your fabric.mod.json's depends section as well)