How do I determine how much weight an indoor hammock mounting kit can bear?
Some general comments:

Single point loads of 200lbs on a single stud (1/2 the rated full load, since you will use 2 anchors) is significant.  Such a mounting would be dependant on securing the lag bolt near the center of the stud.  That can be hard to do, even with a stud detector.

Wall connections: Exterior walls are much stronger than interior (partition) walls. Connections across a corner or across a room will be stronger than a single wall.

Ceiling connections: Connecting perpendicularly to the joists will be stronger than parallel to them (spanning several is discussed below).

Ceiling mounting may be complicated by double mounting to a single joist.

Some specific comments:

My suggestion is to have each attachment point span 2 studs or 2 joists.  This would be simplest by connecting a cross member (such as 2x4 lumber).  Make each support piece longer than the stud/joist spacing by 25% (so the screw holes have strength)  Predrill and use 4 mounting (2 Each end) lag screws, make sure they are centered on each stud/joist and embedded sufficiently.  

Then connect the hammock kit as directed.