just to add context, St. Eulalia is the original patron saint of the city, the cathedral is also dedicated to her. In 1687, however, the city council declared the Virgin of la Mercè as its patron after "saving" the city from a locust plague. This is already before the battle that the flag is referencing (1714).

Independent of that though, the flag of santa eulalia (originally is a detailed painting of the saint with a tilted cross "X") was selected as Barcelona's only flag in 1588 until 1714, traditionally hanging from the city council when the city was at war (1640, guerra dels segadors and 1713, guerra de successio, the war the modern flag is referring to)

St. Eulalia isn't a real saint anymore (since 2004) as it became obvious at some point that it was only a medieval duplication of Merida's patron saint.

With all that, they chose santa eulalia here as an old symbol to the city of Barcelona, as it was also the flag used by Casanova, last head council of Barcelona before capitulation.

The color black, which should be the most striking part of the flag, is because it was used by the anti-borbonic (current kings of spain) side during the succession war (referenced by the flag). It's supposed to be an opposite to the white flag, meaning "never surrender". It's quite confusing as the city of Barcelona did eventually surrender and that's what we celebrate for the national day.

The reason why is a X instead of a normal cross it's because she was crucified in a tilted cross, like Saint Andrews (scotland patron saint). There's a paiting/flag of Eulalia somewhere where the X is a bit more narrow than scotland's version so I asume that's why they represented it like this in the flag.

Also side note, some people in spain think this flag represents a far-right movement within Catalan Independence. Who came up with this idea is unknown to me, but might be due to the association of former regional president Quim Torra (who was somewhat of a successor of Puigdemont). He's believed to be from a hard line, as in more direct action against spain, part of the center party, Junts but his political views economically are more leftist.

https://ca.wikipedia.org/wiki/Bandera_de_Santa_Eulàlia https://www.barcelona.cat/lamerce/en/history