What does 高举旗帜 mean?
I think a little more context is necessary to answer this question.


  The theme of the Congress is: Remain true to our original aspiration and keep our mission firmly in mind, hold high the banner of socialism with Chinese characteristics ... and work tirelessly to realize the Chinese Dream of national rejuvenation.


Ah. So it's not a literal flag we are talking about here, but rather a symbol of socialism.

If we take a look at definition 1.2 of the word "banner" given by OED, we will see that it means:


  Used in reference to support for a belief or principle.
  ‘the government is flying the free trade banner’


Using this definition, the term banner definitely seems appropriate in this context.

"But isn't there already a flag for socialism? Why complicate things by calling it a banner?

As others have pointed out, the phrase “高举 ～ 旗帜” can't be taken literally here. Xi is not asking everyone to physically wave a red flag around, but rather to carry high and proud a representation of one's beliefs. If we pull out the prescriptivist bible OED again, we can see that the english word "flag" is less commonly used to represent an ideology, but rather a physical landmass or position marker. 

This isn't to say that the word "flag" doesn't make sense in this context. Sure, most people would understand the metaphor anyway. However, since the word "banner" has stronger connections to "symbol for one's beliefs/ideologies" than the word "flag", I believe that the word choice they have made is more suitable in a pragmatic, if not literal sense.