Edgehog63 is going to have much better info than me, my DS, a '24 just found out he made the team last night. I will share a brief overview of what I learned.
Flying Team competes in NIFA competitions.
https://nifa.aero/ There are ground events and flying events that you can read more about on the website. Seems like Regionals are in the Fall and Nationals in May (usually, with COVID who knows). For USAFA Flying Team, Seems like you need to be ok with waking up early on Saturdays to get down to the airfield and there are afternoon practices during the week as well - it is a significant time commitment so understand that.
The team typically consists of 36 cadets, 9 from each class. Though this year the '24s had 8 slots as a upperclassman returned. There will be Blue Rush in the fall and Doolies can visit with different clubs/groups at USAFA during the event and this where my DS made first contact with the Flying Team. He signed up and attended the follow-on sessions. Throughout the Fall and Spring, applicants will attend practices - they tend to be vague about the practices and application process so I will respect that and not get too specific. But, I will say for my son, there were a series of practices/tests, an interview, and a flight over the course of about 6 months. I think he said about 80 started the process. Your GPA is a big factor along with MPA and athletic GPA - if you are deficient and ineligible to participate, then you cannot help the team so if you have low scores, you will probably not make the cut. According to the Handbook, min 2.75 GPA, 2.3 PEA, and 2.5 MPA.
My son began his PPL before his Sophomore year in high school. He could only fly in the summer for the most part and only when he had enough money to pay for it so it was a bit inefficient - every summer when he would start up again, he needed a few flights to re-establish his proficiency. He got his PPL in December of his Senior year of HS. He did not fly at USAFA until the tryout. COVID was a pain, there are limited planes to rent at the Aero club, have to schedule well in advance, find a ride, etc plus weather plus he was hitting the books. Getting your PPL while a Doolie is supposedly possible. There is no USAFA program for it, but you can sign up at the Aero club for flight lessons and pay for it yourself. I have no idea how my son could have found the time to do it, so earning your PPL before you get there is probably your best bet - but if you can make it happen at USAF then good for you. I also had read that up to 2 spots on the team may be selected without a PPL - do not know how common this is and if the expectation is that you earn the PPL soon after or you are expected to just crush the ground events. Maybe Edgehog63 could shed some light.
Keep in mind that the Flying Team is totally different from the Airmanship courses at USAFA - well technically it is one of the courses (Flight Team is Armnshp 465). In addition to the flying team, there is Basic Soaring, Soaring Racing, Soaring Aerobatic, Jump, RPA and Powered Flight where you get about 20 hours of flight time.
https://www.usafa.edu/app/uploads/CHB.pdf is a great source for all things USAFA. In this case, pages 75-76 & 242-246 in particular. So, even if you are not on the flying team, there are other programs.
Why commit so much time to it? My son loves aviation and wanted to be saturated with it. From other posts on the forum, members of the team in a 'normal' year might get 75 hours of flight time. Not sure how COVID impacted that this year. So, getting flight time and having USAF pay for it is nice. As you accumulate hours, you increase your Pilot Candidate Selection Method (PCSM) score to a point which can help your chance for UPT and ENJJPT selection. Overall, the training and flight time should make you a better pilot. Oh, and you get to wear your flight suit more often so there's that
But, from what it looks like, you have to spend a lot - really - a lot of time dedicated to the flight team so you better just be passionate about aviation. I'm guessing you probably have to put in at least 12+ hours of non-flight time for every hour of flight time. But if you like aviation, and enjoy your teammates, seems like a a great experience.
I do not have any details on how to get selected. Best I can offer is perform really well in your GPA, MPA and PEA. Keep your head up and devote time to your practices. Be yourself and let them get to know you - if selected, you will spend a lot of time together so I imagine one test is: Do I want to spend a ton of time with this person?
Edgehog63 please correct me where I missed the mark.