I don't understand what you mean by "Can I use "ay" for a NG clause?", but I will explain to you the structure of the sentence from the podcast.
"Ang NASA Airborne and Satellite Investigation of Asian Air Quality science mission ay paliliparin NANG apat na beses ang kanilang DC-8 aircraft. " (The "NG apat..." should be "NANG apat..." because "apat na beses (four times)" functions as an adverb.)
That sentence from the podcast uses two "ang"s. Such a sentence may be made and would be acceptable if:
1. The verb is object-focus, but we want to give focus to both Actor and Object.
2. There is no Indirect Object.
3. Both Actor and Direct Object are common nouns or nouns that may be preceded by the article "ang", e.g., ang NASA, ang aircraft.
4. The sentence is stated in the subject-predicate form, i.e., using "ay" between the subject and predicate. The Actor is treated as the Subject and the Direct Object is the subject of the predicate.
Actor/Subject: Ang NASA ... mission
Predicate: ay papaliparin ... aircraft
Direct Object: ang kanilang (DC-8) aircraft
"Papalipar
ín ang kanil
áng aircraft." = Ang kanil
áng aircraft ay p
ápalipar
ín. = Their aircraft will be made to fly.
"Ang NASA ay papaliparin ang kanilang aircraft. (NASA will fly their aircraft.)
We don't usually state sentences that way, and I suggest that you should not consider doing it yet at your level. It's because such sentences can easily be misstated, and you might be misunderstood or sound ridiculous.
The standard ways to state that sentence are:
Subject-focus:
Ang NASA ay MAGP
ÁPALIP
ÁD ng kanilang aircraft.
MAGP
ÁPALIP
ÁD " ang NASA ng kanilang aircraft.
MAGP
ÁPALIP
ÁD ng kanilang aircraft ang NASA.
Object-focus:
Ang kanilang aircraft ay P
ÁPALIPAR
ÍN ng NASA.
P
ÁPALIPAR
ÍN ng NASA ang kanilang aircraft.
Lastly, please follow the advice given by "DenC" on how to correctly express your sentences. Also, there is no "papakain" verb.