Is it possible for a particular thought experiment to have multiple outcomes based on the view point of the person conducting said experiment? Or can a thought experiment never yield multiple conclusions unless there is an inherent flaw in the reasoning?
Useful thought experiments often have different outcomes which present a problem to be solved by advancing the theory in which they are originally embedded. That is often the only reason they persist as more than window dressing for a given mathematical puzzle.
One of the most famous thought experiments we all meet is the Twin Paradox: One twin remains on earth while the other travels to and fro at a speed near the speed of light.
Within the theory of Special Relativity where it is raised, it has two outcomes, depending upon which twin's perspective you take. Each should perceive the other as aging more slowly on every leg of the trip. So each should expect the other to be younger when they meet again. The paradox is what motivates the General Theory of Relativity, which incorporates the notion of acceleration as the bending of time.
Without the experiment having two outcomes, it would offer us nothing.
Likewise, thought experiments like the Grandfather Paradox, where someone goes back in time and kills their ancestor have multiple possible outcomes. They have motivated the Many Worlds or All Paths interpretations of quantum dynamics, and offered challenges to positions like Loschmidt's paradox of temporal reversibility. Again, without multiple reasonably intuitive solutions, the experiment does not accomplish anything.
A thought-experiment is always conducted against a background of assumptions. I might consider as a thought-experiment a situation in which coercive governmental power - legislative, executive and judicial - is removed from society. This is just the situation which anarchists envisage. Ex hypothesi the details of the thought-experiment are identical between myself and an anarchist. (The experiment is only lightly sketched here but could be made more definite, detailed and specific to any degree.)
If I think that human society cannot maintain a tolerable degree of organisation and security without the coercive powers of government, the state of affairs I project from the thought-experiment will be different, probably widely so, from the anarchist who believes that, through voluntary co-operation, all the benefits of government can be obtained without any of the evils if coercive governmental power is removed from society.
To take an example from the literature, John Rawls conducts a thought-experiment in A Theory of Justice (1971) in which contractors behind the 'veil of ignorance' decide on the basic structure of society. Rawls believes that such contractors will agree on two principles of justice (equal liberty and the difference principle). Critics have argued from the same thought-experiment that the contractors could opt for different principles. The main separating background beliefs at work here are different conceptions of rationality.
In both cases the same thought-experiment produces different projections because of divergent background beliefs.
Is it possible for a particular thought experiment to have multiple outcomes based on the view point of the person conducting said experiment?
It is possible, and common, for a thought experiment to have more than one outcome; this possibility allows for the results to be contradictory and create a paradox, which is often helpful in making or illustrating some larger point. There is not necessarily a flaw in the reasoning. I am unclear about whether the personal viewpoint of the experimenter causes the non-unique results.
Nelson Goodman's New Riddle of Induction (1983) starts from premises describing the present and future colors of an object. The result is that observations of one color also confirm that the object might be a second color. The result shows the uncertainties in drawing generalizations from a series of individual observations.
By contrast, Zeno's paradoxes of motion are thought experiments that have unique outcomes. The arrow paradox assumes that at every instant a flying arrow is absolutely motionless, and thus movement is never possible. The premises admit no other conclusion. The paradox arises from the conflict between that conclusion and the common observation of motion.
In short, every time someone asks, "what if", there appears a new thought experiment, and some of these questions produce more than one answer.