Someone came, so I hid. I think they're gone now.
Someone came, so I hid. I think they've gone now.
Someone came, so I hid. I think they've left now.
Do all these sound natural? Which is the more natural one in the context?
(2) is the most natural. If you saw someone's presence as a threat, it would be more idiomatic to say 'they've gone' than 'they've left'.
They are gone would have been acceptable two or three centuries ago, but is now archaic.
All three of these sound natural to me. As for which is most natural, I would rank them as 3 sounding the most natural, 1 the second most natural, and 2 the least natural. They all sound natural though, so if you were to use any one of these three it would sound fine.