I need to spend some time with creative Google searches this evening to see what I can dig up on hip flexor exercises.
Lunges. There are a couple of variations:
(1) Start in all 4s and then step one foot forward, in its "lane," so you now have one knee on the ground, tib/fib lined up behind it, toes can be either tucked under or pointed back, and opposite foot forward, sole of the foot on the ground. How far forward the foot is and how upright your upper body is will change the intensity of the stretch in the hip flexors. What you want to be mindful of is whether your low back is arching excessively, or if it's getting jammed/low back is cranky; you want to keep the pelvis neutral, which means depending on your flexibility, you may need to tilt your entire upper body forward. Notice whether your hips are rotating in one direction. Often, the hip on the leg that is forward also tends to move forward, so you'll want to make sure they're in the same rotational (coronal?) plane. Hands can go on your thigh or you can have them on the ground or elevated on blocks/books. This is low lunge, crescent lunge, and I think yin yoga calls it flying dragon? If your knees hurt on the mat, put a blanket underneath to pad them.
(2) variation: from where you are in the lunge, walk the front foot out to the side (away from the midline) and take both hands to the the floor on the inside of your forward foot. You can stay there, elevate your hands, or lower onto forearms. This is called lizard or dragon.
If your hamstrings are tight, too, you will notice it in the front leg.
Those are the two main ones. There's another one that is super intense. It is a lunge with the front knee bent at a right angle and your back knee is bent and the back lower leg is up a wall, so it's a quad stretch in addition to hip flexor stretch. The pose is called "King Arthur."
I taught yoga for 5 years, but it's been 5 years since then, so pose names are escaping me!
I don't think yoga does anything to strengthen hip flexors in isolation because we're often trying to get people to not cheat with ab/core exercises.