Yes as Jehovah's witnesses they wouldn't want to have emblems or beliefs that don't go along with their religion.
In the past, they actually did go to "war" and in the bible, there is nothing that specifically prohibits it. I'll just paste part of an article that I got at https://www.jwfacts.com/watchtower/war.php - this is just so you know. Most JW's will not care if older articles contradict what is being taught now. They also wouldn't want any emblems of their countries flags since it would represent them worshiping a man made government instead of God's kingdom.
Watchtower justifies Old Testament Jewish war as necessary to cleanse the promised land of infidels. In the same manner, Christian Churches express their engagement in warfare as a role ordained by God. The very existence of Jehovah's Witnesses is a result of the global expansion of Christianity at the end of the sword.
The Bible never specifically forbids Christian engagement in warfare, and since this was such a significant aspect to Bible history, if continued engagement in war had become an unacceptable practice to the writers of the Christian Scriptures they would have stated so. In fact, several New Testament passages indicate acceptance of war.
When military officers came to John for baptism, John did not direct them to leave the service.
Luke 3:14 "Also, those in military service would ask him: "What shall we also do?" And he said to them: "Do not harass anybody or accuse anybody falsely, but be satisfied with YOUR provisions."
At Matthew 8:5-13 Jesus did not turn the soldier away when asking to heal his manservant, rather commending him saying "I have not found anyone In Israel with such great faith" In the account at Acts 10 Cornelius was not required to step down as commander of Roman soldiers before being baptised.
Paul shows that governments have a right to use the sword to prevent bad, and that we should be in subjection to what they demand of us. This would include going to war when called for.
Romans 13:1-4 "Let every soul be in subjection to the superior authorities, for there is no authority except by God; the existing authorities stand placed in their relative positions by God. Therefore he who opposes the authority has taken a stand against the arrangement of God; those who have taken a stand against it will receive judgment to themselves. For those ruling are an object of fear, not to the good deed, but to the bad. Do you, then, want to have no fear of the authority? Keep doing good, and you will have praise from it; for it is God's minister to you for your good. But if you are doing what is bad, be in fear: for it is not without purpose that it bears the sword; for it is God's minister, an avenger to express wrath upon the one practicing what is bad."
Russell recognised this scripture required early Witnesses to engage in civilian service and even attend the front line.
"The early Bible Students took this scripture to mean that if a Christian was drafted in wartime, he would be obligated to put on a uniform, shoulder a gun, and go to the front, to the trenches. It was felt that since a Christian could not kill a fellow human, he would be compelled to fire his gun into the air if worst came to worst." Watchtower 1995 May 15 pp.21-22