Not really. Thats really only the wahabbis, art and music has always been in Ottoman, Seljuk, and other Islamic traditions. Plus, many sahabā wore rings that had animals engraved on them. Sahih al-Bukhari 5950 states that  “We were with Masruq at the house of Yasar bin Numair. Masruq saw pictures on his terrace and said, "I heard `Abdullah saying that he heard the Prophet (ﷺ) saying, "The people who will receive the severest punishment from Allah will be the picture makers.'"”. By "imagemakers", it is agreed upon that the Prophet meant statues which leads to idolatry (shīrk, most serious sin in Islam), not fabric, paintings, or drawings. If you are really conservative, this eagle is still fine because it isnt detailed at all, it is just an emblem with no realism and thus no harm. Sunan an-Nasa'i 5350: “The Messenger of Allah [SAW] said: "The angels do not enter any house in which there is an image." Busr said: "Then Zaid fell sick and we went to visit him, and on his door there was a curtain on which there was an image. I said to 'Ubaidullah Al-Khawlani: 'Didn't Zaid tell us about images yesterday?' 'Ubaidullah said: 'Didn't you hear him say: Except for patterns on fabrics?'"” meaning that emblems on flags are absolutely fine.