This is the sentence: 俺だってね こんなとこ 三枝(さいぐさ)社長に 見つかってごらん。
This is the context: https://streamable.com/qllstq
The name of the drama is 僕とスターの９９日 and that was said at 7:00 minutes of episode 1.
I had learned that てごらん is equivalent to てみなさい or てみてください. But none of the ideas seems to make sense with the context.
Could you explain to me what he meant by 見つかってごらん？
This is in the same vein as "Move, and you're a dead man," which is effectively a little roundabout way of saying "Don't move". A similar construction works in Japanese, too, but with みろ/ごらん:
少しでも動いてみろ、撃つぞ。
Move an inch, and I'll shoot you.
Here (-て)みる is a subsidiary verb which basically means "to try something and see what happens." See: What is the difference between "verb＋て＋みる" and "verb＋(よ)う+とする"?
Likewise, in your sentence, ごらん is superficially a request, but the speaker is presenting something that must not happen using this ごらん. みろ/ごらん followed by a bad outcome is a common pattern.
こんなとこ三枝社長に見つかってごらん。速攻首ですよ。
こんなとこ三枝社長に見つかってみろ。速攻首だよ。(plain form equivalent)Think, if President Saegusa finds me here like this? I'd be fired immediately!
Related: Is 「うそおっしゃい」 to be taken literally here?
(BTW this type of slangy そっこう "immediately" tends to be written as 速攻, although a few dictionaries seem to be starting to say 即行 is also okay.)
It is the same as 〜てみなさい/〜てみてください. It is a suggestion, albeit not in the literal sense. More like "Why don't YOU try it!?!"
Also, the previous statement "俺だってね" and how they parsed the sentence/subtitles may also have caused some confusion.
俺だってね・・・ こんなとこで三枝社長に見つかってごらん？ 即行首ですよ。
The predicate for 俺だってね has been omitted. It would be something along the lines of 俺だってね、こんなことしたくないですよ！ or 俺だってね、困りますよ！
