Heyo @shosseinib !
So, it doesn't seem that brave allows you to set a custom autocomplete url in your search engines section..
I was able to make it work.
If you go to brave://settings/?search=index+other+search
and toggle that on, and then remove your existing Kagi search engine from the site
when you search with the site it will automatically add it back, and then if you make it active on the Search Engines page in brave settings, it should properly work.
Please let me know if this does not work for you.