Authority

The National Assembly is a constitutional organ and forms one part of Parliament. Excerpts from Chapter 8 - The legislature, Part 1 - Establishment and Role of Parliament, Article 93:

93. (1) There is established a Parliament of Kenya, which shall consist of the National Assembly and the Senate. 

As an organ within Parliament, the National Assembly, along with the Senate, exercises the people's supreme legislative authority in Kenya for and on behalf of the people. 

94. (1) The legislative authority of the Republic is derived from the people and, at the national level, is vested in and exercised by Parliament.
(2) Parliament manifests the diversity of the nation, represents the will of the people, and exercises their sovereignty.

Parliament is therefore the only body in Kenya that has the people's express authority to make laws or change the laws that govern them. It must be guided by the Constitution and the will of the people when making those laws:

(5) No person or body, other than Parliament, has the power to make provision having the force of law in Kenya except under authority conferred by this Constitution or by legislation.

For ease of governance, it may at times be prudent and expedient for Parliament (or a County Assembly) to delegate some of its authority to another body, office or person. If and when this happens, full accountability and unambiguity must be maintained:

(6) An Act of Parliament, or legislation of a county, that confers on any State organ, State officer or person the authority to make provision having the force of law in Kenya, as contemplated in clause (5), shall expressly specify the purpose and objectives for which that authority is conferred, the limits of the authority, the nature and scope of the law that may be made, and the principles and standards applicable to the law made under the authority.

The powers of National legislation are extensively vested in the National Assembly. It therefore follows that the Assembly has the constitutional authority to originate any Bill, and to go ahead and pass it for enactment without reference to the Senate, if such a Bill does not concern the Counties. Chapter 8 - The Legislature, Part 4 - Procedures for Enacting Legislation:

109. (2) Any Bill may originate in the National Assembly.
(3) A Bill not concerning county government is considered only in the National Assembly, and passed in accordance with ........ and the Standing Orders of the Assembly.

The National Assembly also has veto powers over a special Bill from the Senate concerning Counties:

111. (2) The National Assembly may amend or veto a special Bill that has been passed by the Senate only by a resolution supported by at least two-thirds of the members of the Assembly.

The provisions of Article 111. (2) appear to emasculate the Senate and are likely to generate widespread protestations from both the Senate and the public. Indeed, when the National Assembly disregarded the amendments of the Senate on the Division of Revenue Bill 2013/2014, the Senators rose with one voice to protest what they saw as an unfriendly (House) peer out to frustrate devolution; perhaps with the foresight that their counterparts may 'interfere' with the subsequent County Allocation of Revenue Bill that must originate from the Senate, but must be considered by the National Assembly. As it is, a special Bill touches on the very heart of the affairs of the Counties (and hence devolution):

110. (2) A Bill concerning county governments is–– (a) a special Bill, ........, if it–– (i) relates to the election of members of a county assembly or a county executive; or (ii) is the annual County Allocation of Revenue Bill ........

The Members of the National Assembly are not under any gag orders that sometimes face the public. They can, and should boldly articulate the issues and interests of the people of Kenya without fear or favour. Article 117 of Part 5 - Parliament's General Procedures and Rules, excerpts:

117. (1) There shall be freedom of speech and debate in Parliament. 

Having been assigned the legislative authority of the Republic, the National Assembly, along with the Senate, is empowered to consider and pass amendments to the Constitution of Kenya 2010. This is a most sacred duty and must not be abused - rather, Parliament must at all times remain guided by the Constitution, defend it, and promote its ideals:

93. (2) The National Assembly and the Senate shall perform their respective functions in accordance with this Constitution.

94. (3) Parliament may consider and pass amendments to this Constitution, and alter county boundaries as provided for in this Constitution.
(4) Parliament shall protect this Constitution and promote the democratic governance of the Republic.

The National Assembly is empowered by the New Constitution to set its own calendar and can legally meet and transact its business from anywhere in the country. Under the Old Constitution, the President determined and set the parliamentary calendar, and oftentimes would use that privilege to manipulate and frustrate the business of the House. Now, within 30 days after the Assembly is constituted, the President is required in writing, to choose the date of the Assembly's first sitting. From Chapter 8 - The Legislature, Part 6 - Miscellaneous:

126. (1) A sitting of either House may be held at any place within Kenya and may commence at any time that the House appoints.
(2) Whenever a new House is elected, the President, by notice in the Gazette, shall appoint the place and date for the first sitting of the new House, which shall be not more than thirty days after the election.

The National Assembly has been vested with the authority to approve a declaration of war or to extend a state of emergency declared by the President. It must consider, debate and vote on any such declarations by the President.

95. (6) The National Assembly approves declarations of war and extensions of states of emergency.

58. (2) A declaration of a state of emergency, and any legislation enacted or other action taken in consequence of the declaration, shall be effective only— (b) for not longer than fourteen days from the date of the declaration, unless the National Assembly resolves to extend the declaration.

(3) The National Assembly may extend a declaration of a state of emergency— (a) by resolution adopted— (i) following a public debate in the National Assembly; and and (ii) by the majorities specified in clause (4); and (b) for not longer than two months at a time.
(4) The first extension of the declaration of a state of emergency requires a supporting vote of at least two-thirds of all the members of the National Assembly, and any subsequent extension requires a supporting vote of at least three-quarters of all the members of the National Assembly.

This is a good provision given that many countries the world over, have been known to go to war at the whims of one person. This authority of the Assembly means that a state of emergency must have the popular backing of the rest of the people (through their elected representatives).