We, Us) Persian Gulf veterans are proud of our service.

a. We

b. Us

Is it we or Us?

I think it is We since you know in the constitution that is how it goes.
We goes with US

We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity

You're right.

Another way to look at is to ask which is right --
Us veterans are . . .
We veterans are . . .

Thanks ! Could you please look at my other post?!

Correct! The correct pronoun to use in this sentence is "we," not "us." When referring to a group of people, such as Persian Gulf veterans, the pronoun "we" is used as the subject of the sentence. "Us" is used as the object of a verb or preposition. So, in this case, since you are stating that Persian Gulf veterans are proud of their service, the subject pronoun "we" should be used.