Is this the right headset for a tapered frame orange five frame?

http://www.tweekscycles.com/components/headsets/hope-technology-zero-stack-tapered-headset-zs44-28-6–zs56-40

I’m a bit confused around zero stack and integral.

Also, would a hope one be best option? Or should I go Chris king or other options?

Yep, that one should fit.

Orange list the headset code as: ZS44/28.6|ZS56/40 – for a tapered MTB fork steerer tube in the 44-55.95zs frame.

I had the same problem back when Hope were having trouble getting lower bearings, so ended up fitting a Superstar Tapered T3 headset as an interim measure, been good enough to not warrant being replaced!!