In this case, かける means put something(must be liquid) onto something. に equivalent to "onto" right here. so if you just say. お酢をかけて食べた。 then they're gonna ask you like. 「何に？」(onto or on what?) like that.

"かける" has many different meanings, but in this case, it means putting/covering/sprinkling... something on an object. So it works like "with" in this sentence. "に" is a part of speech (a particle) which doesn't have any meaning itself. But I feel like it has an image like an arrow? fish and chips に vinegarをかけて食べました fish and chips ← vinegar the school に 行った went to → the school friends に 会った met → my friends Hmm.. I hope it'll help

I imagine "on the fish and chips" when I say "かける" (e.g. サラダにドレッシングをかける)。 When we say "フィッシュアンドチップスにお酢をかけてたべる", we eat fish and chips with vinegar and so I think "with" is also correct.