go fry a stale egg

Raymond ChandlerのPLAYBACKを読んでいます。会話の中に慣用句と思われる表現が出て来ました。
"Very funny," Goble said, sneering. "And how did you know his name?"
"On account of somebody called him by it. That would be too funny, wouldn't it?"
He sneered. "I told you to stay out of my way. I know who you are now. I looked you up."
I lit a cigarette and blew smoke in his face. "Go fry a stale egg."
"Tough, huh," he sneered. "I've pulled the arms and legs off bigger guys than you."
LとRの発音の区別が苦手は私は "Go fry a stale egg" で "Go fly a kite" を連想してしまいます。 意味も同じようですが、どうでしょうか？　辞書で確認します。
"stale" は入っていませんが、 "Go fry an egg" の説明があるのを次の辞書で見つけました。
・McGraw-Hill Dictionary of American Idioms and Phrasal Verbs: Go away and stop bothering me! Go away and stop bothering me. Go fry an egg! Get out of my way! Go fry an egg!
"Go fly a kite" と同じですね。