The short answer as to who can fly in the NFZ would appear to be - file a flight plan.
The longer answer would appear to be:
“4. Authorizes Member States that have notified the Secretary-General, acting nationally or through regional organizations or arrangements, and acting in cooperation with the Secretary-General, to take all necessary measures, notwithstanding paragraph 9 of resolution 1970 (2011), to protect civilians and civilian populated areas under threat of attack in the Libyan Arab Jamahiriya, including Benghazi, while excluding a foreign occupation force of any form on any part of Libyan territory, and requests the Member States concerned to inform the Secretary-General immediately of the measures they take pursuant to the authorization conferred by this paragraph which shall be immediately reported to the Security Council;
“5. Recognizes the important role of the League of Arab States in matters relating to the maintenance of international peace and security in the region, and bearing in mind Chapter VIII of the Charter of the United Nations, requests the Member States of the League of Arab States to cooperate with other Member States in the implementation of paragraph 4;
“No-fly zone
“6. Decides to establish a ban on all flights in the airspace of the Libyan Arab Jamahiriya in order to help protect civilians;
“7. Decides further that the ban imposed by paragraph 6 shall not apply to flights whose sole purpose is humanitarian, such as delivering or facilitating the delivery of assistance, including medical supplies, food, humanitarian workers and related assistance, or evacuating foreign nationals from the Libyan Arab Jamahiriya, nor shall it apply to flights authorised by paragraphs 4 or 8, nor other flights which are deemed necessary by States acting under the authorization conferred in paragraph 8 to be for the benefit of the Libyan people, and that these flights shall be coordinated with any mechanism established under paragraph 8;
“8. Authorizes Member States that have notified the Secretary-General and the Secretary-General of the League of Arab States, acting nationally or
through regional organizations or arrangements, to take all necessary measures to enforce compliance with the ban on flights imposed by paragraph 6 above, as necessary, and requests the States concerned in cooperation with the League of Arab States to coordinate closely with the Secretary General on the measures they are taking to implement this ban, including by establishing an appropriate mechanism for implementing the provisions of paragraphs 6 and 7 above,
A.
EUROCONTROL actions following UN Security Council resolution on Libya | EUROCONTROL
Therefore only those flights which are exempted from the ban, in accordance with the resolution, will be permitted to operate.