YES you can flat spin and RV ... at least a RV6A ... DON'T DO IT! I took me little over 5000 feet to recover.
Then you did something wrong for the first 4,000' or so. It wasn't the airplane. But I'm glad you figured things out.
Flat spins are very misunderstood. There is no such thing as a 'flat' or non 'flat' spin - only varying degrees of flatness, ending with the nose level with the horizon. The video referenced above is only
very mildly flattened due to the very low power setting. Most aerobatic airplanes will not flatten out simply by letting a normal power off spin develop. They require flattening inputs, and will only signifcantly flatten in one direction. With Lycomings and upright spins, that's with left rudder. Right rudder inverted.
The airplanes you want to avoid developed spins in are the ones that will flatten out on their own and become unrecoverable. Unfortunately, nobody knows what all these types are, since few GA aircraft are fully spin tested. Don't do spins in unapproved aircraft or those for which spin characteristics are unknown. I would suggest against spinning anything with full wing tip tanks.
Google 'Tipsy Nipper flat spin' for an interesting video and story. The issue with very flat spins is that there is very little airflow moving across the rudder to oppose the yaw.
Back to RVs - You may be entering test pilot territory by deliberately applying inputs to produce as flat a spin as possible. After establishing a normal left rudder power off spin, this would involve full aft stick, full right aileron and full power. I don't know of any RV pilot who has done flat spin testing at the edge of the envelope, and has sufficient spin expertise to provide good information on them. But maybe there are some of you, who maybe just haven't spoken up here in the past on this subject. I'd be interested in the information since I no longer have an RV to play with. Nearly all aerobatic airplanes will recover from flat spins. You will not necessarily die. But in aerobatic airplanes, flat spins are a gyroscopic maneuver, done intentionally.
Unless you have had advanced spin training specific to the aircraft you are flying, your best bet for recovering any type of spin (assuming you maintain situational awareness) is PARE. If you have lost situational awareness, your best bet is to pull power off and neutralize (move to center) all three flight controls, and wait for recovery.
That being said, the most efficient ACTIVE flat spin recovery method for most aerobatic airplanes is full power, opposite rudder, stick forward to some degree, and in-spin aileron. Yes, I know we all learned that you should always pull power off for spin recovery. Don't misunderstand - I'm talking about ACTIVE recovery via refined practice. This is very different from the concept of
emergency spin recovery technique, which absolutely should involve pulling power as the first step.
In-spin means aileron in the direction of the roll component of the spin, not necessarily the yaw direction (inverted spins). But by all means, if you have tried PARE, or pulled power off, centered all the controls, and are not recovering any type of spin after 5+ seconds have passed, you need to try something else. The Tipsy Nipper pilot that I mention above did just that, and it saved his life. But this aircraft had unusual spin characteristics, atypical of most aerobatic aircraft.
Keep in mind that with metal props, high power flat spins apply a LOT of gyroscopic stress to the crank flange. I would NOT recommend anyone here go play with these unless you have a high level of expertise and experience with advanced aerobatic spins and are willing to play test pilot. If this describes you, then nothing I'm writing here needs reading. There just isn't an existing knowledge base with the entire spin matrix in RVs as there is for more serious acro ships (Pitts, Extra). Until that knowledge base exists, I'd tread cautiously. By 'knowledge base', I mean the full matrix of spin testing across all aerobatic RV models, across the
entire acro W&B range.
I never tried serious flat spins when I had an RV, but I strongly suspect that any aerobatic RV model, properly loaded, will recover from a fully flattened spin (full power, outspin aileron) by pulling power off and neutralizing the controls. It should recover a little more quickly with normal PARE. Folks have been known to produce accidental inverted flat spins by kicking too early on hammerheads and being way too aggressive with forward stick (full forward stick). Folks have also gotten into accidental inverted flats doing shoulder rolls. There was a fatal Skybolt crash this year associated with that. Accidental upright flat spins are uncommon. I can't think of a likely scenario for encountering an upright flat spin while doing RV acro.
Be aware that many airplanes strongly react to even simple aileron inputs, forgetting full power. The Clipwing J-3 Cub I used to fly had extremely straightforward spin characteristics - just like a standard longwing Cub. Fully-developed, recovery was within 1/4 turn. But if you applied full right (outspin) aileron during the left rudder power off spin, it would flatten slightly. The rudder then felt eerily disconnected with almost no pressure. After applying opposite rudder, in-spin (left) aileron, and forward stick, it took nearly a full turn to recover. Big difference in character compared to a neutral aileron spin. It's been a long time since I've done spins in RVs and I don't remember the specifics on how aileron-affected the spins were, other than simply accelerating the rotation a bit.
Bottom line in any aerobatic airplane, if you pull power and neutralize the controls the moment the airplane breaks loose or otherwise starts doing something unexpected, you will almost immediately recover. Admit you have lost control and don't fight the airplane.
Get good aerobatic/spin training.