えっ、私が運転手ですか
ああ、社長専属の運転手が体調を崩してどないもアカンらしいねん
My attempt at a translation:
Huh, me a driver?
Yes, the president's personal driver is not feeling good
In the standard dialect, "どない" would be "どう", "どんな(に)" or "どのよう(に)".
And "どないも" would be "どうにも", meaning "no matter what", "for one's life", "if one's life depended on it", etc.
So the line translates to something like
Yeah, I'm hearing the president's driver isn't feeling well and no good (for work) if his life depended on it.