Just shut up with いいから

Vocabulary Explanation: Don't worry about it with いいから

To allay Haibara’s fears of being recognized at an event, Conan lets her wear his fake glasses as a disguise. After she’s kidnapped, Conan communicates with her through the wireless communication device built into the glasses, in hope of discovering where she’s being held. Once Haibara confirms she cannot escape the room she’s in, she tells Conan to listen carefully and starts listing off the details of her research around the drug that caused the two of them to become children.

コナン:: 「おい、やめろ！！　んな事(こと)おまえがそこから脱出(だっしゅつ)したら聞(き)いて…」; “Hey, stop it!! I'll listen after we get you out of there...”
灰原:: 「いいから黙(だま)って聞(き)きなさいよ！！」; “Just shut up and listen to me!!”; Literal: “It's fine, so shut up and listen!!”

Key Points

1いいから = enough with that

In this scene, いいから does not mean “because it’s good” or “it’s fine” literally. It is a forceful way to cut off what Conan is saying and push the conversation forward.
Here it works like “Enough, just…” or “Just…” before the command that follows.

2The line is really two commands

「いいから黙(だま)って聞(き)きなさいよ」 is basically “Stop arguing about that, be quiet, and listen.”

3黙って links into the next action

黙(だま)って is the -て form of 黙(だま)る, so it connects to 聞(き)きなさい.
The sequence is “be quiet and listen”, not two unrelated fragments.

4聞きなさい is a firm order

〜なさい is a commanding form often used when speaking down to someone, scolding them, or giving a strong instruction.

5Sentence-ending よ adds insistence

The final よ pushes the command at the listener and makes it sound more emphatic.