According to the Central Civil Services Conduct Rules a central government official may not be allowed to engage in any occupation, profession or vocation which provides him with any income. If any employee violates the said provision in The Conduct Rules it calls for disciplinary actions against them which eventually may result in their removal from service.
A central government employee can also be allowed to start Youtube channel provided, as per Central Civil Services Conduct Rules that the channel does not comment on central government policies and does not make use of any resources and information to which the employee has access by being employed there.
In addition, standard law regarding freedom of speech is applicable as to any citizen of India namely no seditious activity, no porn, anti religious or regional inflammatory etc. However, one can better be on the safe side to take permission as taken by poets and other authors who are civil servants, artists who can act in dramas or sports persons in government employment.
It also depends upon the terms of employment in the current organisation. A Youtube channel counts as a business in its own right and if the organisation prohibits entering a business while in office, then you may not be able to start one. Check the terms of your contract or talk to the Human Resources Department for the clarity of the terms of employment whether such exclusivity clause exists or not.
Reference: Central Civil Services Conduct Rules