How do I use the phrase, "By way of" correctly?

I wouldn’t use “by way of” in this context. I would simply say “American national born in the Philippines.

I use “by way of” and understand it to be a phrase describing directions. “You can go to Boston by way of New York City on the train, or you can go by way of the highway by car.”

Synonymous with “via,” as @Hawaii_Jake shows in his examples.

Also:

“By way of illustration, the professor drew a picture on the board. He read them a passage from Shakespeare by way of example”: Source

Ahh! Thanks you two!

I agree “by way of” usually is a place you pass through, not originate. Although, if you said you were Anerican by way of being born on base to American Parents in the Philipines it would not sound odd to me, I would know exactly what you mean, and would not think to correct it. It’s kind of a cute way to state it in my opinion. Kind of like you did start out as American, born to American parents, but the birth makes it a little tricky since so many Americans are obsessed with being born on American soil.

If I were you I would just say I am American. Are you searching for a simple way to convey you were born on base in the Philipines? I assume, but assuming never works, that you want to tell people you were born in the Phillipines on a Navy base as part of your identity?

@pleiades So I was born in the Philippines on an American base. Father served in the Navy.

Sometimes we forget that language is for communication; I think you described it very well.

I’m an American (I’m guessing) Navy brat born in the Phillipines.