[Oratam]

I think to be a phoenix proper it needs to have flames at the bottom out of which the bird rises.

I think the pin resembles the eagle atop the globe on the mace uswd by the sergeant at arms of the House of Representatives.

[Miss Didi]

President @RealDonaldTrump’s 2020 #Salute2America will be a patriotic tribute to our men and women in uniform, and the @DeptofDefense will be providing a one-of-a-kind air show! https://t.co/hmBirMxrqM pic.twitter.com/jnlbG8ALLC— Secretary David Bernhardt (@SecBernhardt) July 1, 2020

[Aquamarine]

The phoenix has a longer neck than the eagle. Here's a funky video on the pin

[sweetiepiezer]

The sergeant of Arms in the House Of Representatives is in charge of the Mace.
It is kept in his office what is not on the floor of the House.

I was in his office once and I got to hold the Mace.

I have a picture of me holding it. Quite a tour I was on.

[thinden]

Looks pretty similar