How to make sure wooden bar is stable enough to mount hammock chair?
The horizontal board (rafter tie) and roof boards (rafters) are sized large enough for your purpose. The connection between the two is also adequate.

I don't think it necessary but if you were to want to increase the strength then I would start by adding (2) #8 x 3" screws to the connection from the rafter tie to the roof rafter. For more, I would suggest sharing the load with more rafter ties by placing a 2x4 or 4x4 over the top of (2) rafter ties (if you want to hang the chair between rafter ties) or over (3) rafter ties (to hang directly from a rafter tie as you plan). This can be attached with #8 screws (they are not structural, they just keep the board from moving)