Can I say ' I am to be doing'? Similarly, I have to be doing' Is it possible in any sense? Can you refer me any book in which you saw this use?
What you're talking about is variations on the future progressive (or continuous) tense.. This is used to describe ongoing action that will happen in the future. As such, it's not common since the simple future tense is sufficient, but is is used:
If you are going to use it, however, you should establish some kind of parallel time frame to show that your action is continuing at the same time.
Tomorrow I will be preparing my lessons by myself since my wife will be out visiting her family.
Next week I am to be spending time with my entire family while they are in town for the holiday.
Next year I have to be traveling a lot more for business while [something else is going on]
It's difficult to come up with good examples for these since it's easier to write them using the simple future tense:
Tomorrow I am going to prepare my lessons by myself since my wife will be out visiting her family
So while it is possible to use these verb tenses, I don't recommend it.
[Edit] "Have to be doing" could be either present or future tense, depending on how it's used. It suggests a requirement to do something, either now or at some point in the future.
Although I would rather be out playing, Mother says I have to be doing my homework.
Although again "I have to do ..." is generally simpler and more clear.
Although I would rather go out and play, Mother says I have to do my homework.