There is some flexibility in the use of future simple and future continuous thin this kind of sentence, but I think that future simple would be better.
You generally use "will start" if you know exactly when something is planned to start.
Note also that, when the guide announces something, it is reported speech, so we backshift will to would and is to was.
The guide announced that the tour of the museum would start in 10 minutes and was scheduled to run for about two hours.
You generally use "will be starting" if you are not sure exactly when something will start, for example
We need to hurry up... the tour of the museum will be starting soon!
You are probably thinking that "is scheduled to" is a passive voice form of "the guide scheduled the tour" which is past tense, and so it should be "was scheduled to". In fact, [scheduled] in this context is an adjective, meaning "planned to happen at a particular time". So we use present simple because, at the moment, the schedule says that it will happen at the specified time, even if the scheduling happened in the past.