PBSteve: Thanks, helpful links. These things may be applicable to other prop projects. It looks like my RFID problems will be solved soon.
After reading FallNAngel's comments I looked at simpler stuff for the RFID reader. In terms of difficulty I would like to stick with a Pi, but by looking into the possibility of using an Arduino for reading RFID tags I discovered a solution to my RFID power problem. You see, the root problem was that I am an idiot. Went to USB control because many of the things I worked with in the past were easier and better that way. There are RFID readers for the Arduino that also work fine the Raspberry Pi and it turns out that hooking them up is just a matter of plugging in cables in a few pins. Also some of them even have Python libraries already created. So the reasons I bought the USB RFID reader were erroneous -USB was not the only to get easy to install/easy to programme hardware. I plan on buying one of these modules and selling my USB reader. That means I just have to power the Pi, so no problem. Also, many of them work with the Raspberry Pi Zero, the cheapest thing out there.
FallNAngel, I know that overall it is true, it is overkill. Issues of cost and ease of use cannot be ignored though. Cost is in practice zero when I use a board I have around not doing anything else and that is usually a Pi. Being able to use Python makes things so much easier. However, I sometimes think I should use an Arduino or Teensy or somesuch for a prop just to force myself to experience and learn it. It might put me in a better position to avoid overkill all the time in the future.
I am not married to the sound idea, but I found battery powered speakers and thought it adds minimal power and brought it one more step to a wow factor.
As for the lights, no, a tiny, single LED bulb is not enough. Just like you were worried about not hear anything over the battle going on I wanted players from far and away to know that a flag is a certain colour. Also one of my design goals was to make it look and seem like a flag. The electronic flags would be big, illuminated flags. A LED strip is the only way I found so far to get light all over the insides of my plastic flags and their plastic poles. I can forgo most of the superficial stuff on other props, but the flags have to have a bit of of a wow factor to their appearance when turned on. Originally they were to be built for a charity game so the idea was to impress the players with the new gadgets. Make them more likely to donate and come back the next year. Was unable to do it on time for that, but I still want to make a glowing flag design not just a machine that tracks who pushed a button.
I really looked into it and studied photos showing the tree density at my favourite fields, etc. WiFi is just not enough. For non Flag projects the fact that the ESP8266 can be both a client and access point at the same intrigues me. Synapse modules are basically me going the RF communication route. I am pretty close to giving up on them though. Might try LoRa next. In fact, thanks to you suggestion I found some very cheap LoRa modules on Aliexpress.
If I felt like it I can kill the sound, but the fancy lights are necessary and controlling them is hard, so I think for the flags it is Raspberry Pi units for now still. This conversation is making me think about doing more research again just to see if there is just as a good a way with Arduino or similar. Also, it makes me think more conciously of what I had in the back of my head for a while -the next prop should be Arduino based.
As for my new RFID approach, I already have 6 RFID tags that I really like. They are 3cm discs with a hole in the middle. However I am having trouble finding a reader that connects to the GPIO pins and is a small unit and does the format of these discs. They are 125khz EM4102. Plenty of 125khz readers, but none that do EM4102. Looked at RDM6300 but one vendor (Canada Robotix) told me it only does EM4100. It would be a shame to rid of these so easy to mount into props tags but it looks like I will have to sell them with my reader. Focused on 125khz because of the discs I have, but if I cannot used them then I use the common RC522 modules as there are many tutorials for them and they are quite cheap. (They are 13.56Mhz.)