Much like Captain America himself, many of the Sentinel of Liberty's rivals and opponents represent some sort of nation or ideology. These include the Nazi Red Skull, the jingoistic U.S. Agent and Hydra operative Baron Strucker. The same is definitely the case for the Flag-Smasher.
Defined by their opposition to the world's various political agendas, the Flag-Smasher identity has been taken up by a myriad of different people. Many of them have fought Captain America, while others have taken on different heroes. They appear as a group in the Disney+ series The Falcon and the Winter Soldier, with their leader being based off of the most prominent Flag-Smasher in the comics. Here's the not-quite star-spangled story behind the villain without a country.
Karl Morgenthau
The original Flag-Smasher debuted in Captain America #312 and was created by Mark Gruenwald and Paul Neary. His real name was Karl Morgenthau, and he was the son of an incredibly wealthy Swiss banker. Upon seeing his father get trampled to death in a political riot, he vows to fight against the idea of countries, patriotism and nationalism. He forms an organization called ULTIMATUM, fighting nationalism and patriotic symbols the world over, particularly in New York.
A hostage scheme draws the attention of Captain America, who tries to reason with Flag-Smasher and get him to rearrange his attempts at world peace into a more peaceful capacity. These attempts to find a common ground fail, but Flag-Smasher does eventually team up with Steve Rogers to save John Walker, the newest Captain America, from the Red Skull. The Skull had been secretly financing ULTIMATUM, leading Morgenthau to a moral crisis. He would briefly gain superpowers, but these eventually wore off. This version of the character would apparently be killed off down the line by X-Force member Domino, but he would inspire Karli Morgenthau, the female MCU character who leads the Flag-Smasher group.
Guy Thierrault
Guy Thierrault was a member of ULTIMATUM who took on the role of Flag-Smasher after the original's assassination. He wouldn't have much success in the role, however, seeing a series of defeats at the hands of young heroes. These included the Runaways, Spider-Girl and the Liberteens. When he and his group tried to take down Agent Venom, he responded by killing Flag-Smasher's men and eating his arm.
He would eventually cross paths with Deadpool, with the Merc with a Mouth mercilessly defeating him. In response, Thierrault was killed by one of his own men.
Carl
This new Flag-Smasher was named Carl, perhaps in reference to the original. He killed Thierrault because he obeyed Deadpool's demands to never strike back at him. This was despite Deadpool blowing up a helicarrier with the loved ones of several different ULTIMATUM members.
In response, Carl killed his leader and took his place, promptly leading an assault on one of Deadpool's allies. This failed, with Deadpool setting his own trap for Flag-Smasher and his group. One by one, he killed every last one of them, leaving Carl for last and shooting him in the head.
Life Model Decoy
The newest Flag-Smasher showed up to disrupt a gala honoring a conservative politician, with his terrorist antics meant to recruit both Steve Rogers and Sam Wilson for ULTIMATUM. His plans involved erasing the names from the US No Fly List and obtaining the nuclear launch codes. Falcon and Rick Jones are able to take down the bombs planted by ULTIMATUM, but Flag-Smasher escapes before he can be defeated.
This is revealed to actually be a mere Life Model Decoy sent by Steve Rogers to test his own increasingly questionable loyalties. Since then, no new Flag-Smasher has shown up to face Captain America, though the TV reimagining of the concept may see that change in the near future.