My flexibility training for climbing has primarily focused on two areas: groin (side splits) and hamstring.

I've seen really fast gains from strength-at-range training, which basically attempts to strengthen the muscle at the limit of its range of motion. The reasoning I've heard for why this is effective is twofold:

1. Your central nervous system will hold you back from stretching beyond where it feels strong to prevent you from hurting yourself, so strength is somewhat surprising limiter on flexibility. I should note that this is effectively hearsay: while I've heard this from a few reputable sources, I'm not aware of any scientific way of proving this.
2. It doesn't matter for your climbing if you're able to get your foot into a certain position if you're then unable to pull from that position. This is analogous to problems with out-of-context finger strength, where you may be able to grip a hold but not move off it, because the arm system as a whole is unable to maintain strength while changing position.

Because strength at range exercises stress the muscle as it lengthens, they are particularly likely to cause delayed onset muscle soreness. You can see DOMS for more information, but the takeaway is to start with low weights, and do a light version of the workout a day or two after; the chemical reactions which cause DOMS also have a preventive effect which treats existing DOMS and prevent further DOMS.

Side Splits

A key here for me has been understanding a particular gotcha of the side splits. There's a bony protrusion on the outside of the femur, and when toes are forward and pelvis vertical, splitting the legs causes this bony protrusion on the femur to run into the pelvis long before you reach the full range of motion of the muscles. Before I knew this I ran up against this for a while, seeing no progress in my side split and even causing a bit of pain which would cause me to stop stretching at times.

The solution to this is to bring the pelvis into a right angle with the femur, which puts the bony protrusion behind the femur. There are two ways to do this:

1. Point the toes and knees out instead of forward. It's really the knees that are connected to the femur, but the knee is not a ball joint so if you don't align the knee with the foot you're going to have problems.
2. You can also tilt the top of the pelvis forward. Note that this doesn't necessarily entail tilting the entire upper body forward.

There are three exercises which I use:

1. Butterfly which hits the muscles of the groin which are most active when the knee is bent (TODO: get the names of the muscles and maybe some pictures?). With your butt against a wall, place dumbbells (starting at around 10lbs or 5kg) on your knees in butterfly position. Extend to your range for 3 seconds relaxed, then flex the muscle, bringing the weight up just a tiny bit, for 3 seconds. Do this for 2 sets of 20 reps each.

   Progressing this exercise is a bit tough: raising the weight is easy but I've quickly gotten to the point that my knees are resting on the ground while not fully extended. Elevating by sitting on a 45lb barbell plate has allowed my to drop my knees further, but now my shins are running into the plate and I'm haven't found a good narrower surface to sit on. I'm not too worried about it at the moment because I can still progress strength without progressing range (higher dumbbell weights), and this isn't the position which is most relevant to climbing.

2. Wide squats This hits all the muscles of the groin in a position which is somewhat relevant to climbing. You can "heel-toe" your feet out to get a rough measure of width, then holding a dumbbell (starting at 10lbs or 5kg) squat down as far as you can, remembering to tilt the pelvis to avoid the femur colliding with the pelvis. When your femurs are horizontal, you can go wider. Hold for 3 seconds at the bottom of each squat, and do 2 sets of 20 reps each.

3. Unsupported splits Hits the muscles of the groin which are active with straight knee. With the body upright-ish, spread the legs straight to a position with a light stretch: you can spread the toes to avoid the femurs colliding with the pelvis, but for balance purposes it may be beneficial to tilt the pelvis forward a bit and keep the toes pointed partly forward. Then, importantly, don't support your hips with your arms: keep your hands away from your hips, legs, and lower torso. Instead, support your weight with the muscles of the groin.

   You should aim for a width where you can hold the position for about 45 seconds: if you're able to hold it for 60 seconds, you can go wider, if you're only able to hold for less than 30 seconds, you should ease off a bit. Do this twice.

   Tracking progress isn't strictly necessary unless you believe you are hitting a plateau and want to verify this. You can track progress by taking photos and measuring angles, or measuring foot width on the ground with tape. However, if you just go to the end of your range and hold there, you'll probably find holding this challenging.

   It's also not necessary to add weight to this, because as your feet go wider, your muscles are at a greater biomechanical disadvantage due to the lever physics. It's quite common for an increase in range to greatly decrease how long you can hold the position, as the strength required increases greatly with even a small increase in range.

Hamstring

A peculiarity of the hamstring is that it's difficult to isolate since it works in conjunction with the entire posterior chain. The glutes and calf can loosen as you stretch the hamstring, causing you to have to increase the intensity of the stretch midway through, so it's beneficial to stretch these muscles before you stretch the hamstring. It may also be beneficial to stretch the distal hip flexors (pigeon pose) and/or the groin for similar reasons.

I've been doing offset-leg good mornings to work these, however I'm not as happy with the results. I've experimented with good mornings on one leg with the other ankle tucked above the knee; these seem only slightly more effective and have balance issues. I'd like to experiment with nordic leg curls but these require a barbell.

Opposing muscles

It's worth noting that while the groin and the hamstring do the lengthening and then pulling at that range, the opposing muscles (distal hip flexors and psoas, respectively) have to be strong enough to get the leg into position. To work these I occaasionally do fire hydrants and standing forward leg lifts.