The Banner: Republic (Large) decoration can be bought for 200 credits. It can be bought from a vendor in a room with a guild bank in the Crafting & Strongholds section of the fleet, NOT in the PvP section of the fleet. It does not require any special skills or PvP to acquire, just credits.
This item can be bought and sold on the GTN - beware of scammers and don't buy it from the GTN unless it is less than 200 Credits.
The Banner: Republic (Large) decoration used to cost 200 Warzone Commendations, but Warzone Commendations were removed from the game so now it just costs 200 Credits.
You can only buy this banner from the vendor on the Republic side, so if you mainly play an Imperial character you will need to level a Republic character past their starter planet to get to the fleet. If your new Republic character is low on credits, send some over from your Imperial character by mail.