The hip flexor muscle you're talking about sounds like the psoas. Often aka iliopsoas because it's so parallel/snug with the iliacus muscle, you can vicariously help relax this muscle by using a little massage just on the inside (medial side) of your anterior superior hip-bone sticky-outy spot over by your navel. (Technique: Feel that hip bone, might want to use the opposite-side hand, and push in a bit along the inside/medial side until you feel the muscle on that part of your pelvis. Hold a spot for a good couple of minutes using just a little pressure than you feel like you really want to, while taking deep breaths, then move to the next spot and hold again. Don't rub around too much, a little feels good but a lot will overwork it.)
The stretch I'm going to recommend looks an awful lot like a simple lunge but the important part is more subtle than that.
Anyway, look at the anatomy of the psoas/iliopsoas to familiarize yourself and get the good visual in your head of what you're working with: https://i.ytimg.com/vi/cHWjpQ06-cE/maxresdefault.jpg
Specifically psoas, this will really help with you getting the stretch right: http://static1.squarespace.com/static/540777f2e4b0cd91b7e809db/t/5474fb89e4b00c9dcf563b20/1416952713801/psoas-profile
And now, the type of stretch -- it's basically a lunge, except you don't overdo it with the distance you're lunging, it's not about bending your knees or bending down or engaging your hips, it's just about hyperextending the hip to be stretched. Then, once in a mild lunge position with the intended hip hyperextended and stable, one slowly rotates the bottom of the pelvis forward, or tucks one's tail as it were, and pushes on the psoas from behind, stretching it out over the pubic bone. See: http://2.bp.blogspot.com/_ECTa4dlGnQo/SyO17eBTG9I/AAAAAAAAAWI/pBioAQzE3vo/s320/psoas+stretch+4.png This is a good example of how not-exaggerated your stance should be, and also I really personally do like the feeling of raising my same-side arm partway through the stretch in order to help extend the stretch throughout all my fascia and my whole core on that side.
Also, two VERY IMPORTANT protips for your technique when doing any kind of stretching or massage at all:
Hope that's helpful! I'm glad I happened to surf past this sub thanks to an unrelated link today. Didn't want your thread to go all neglected and stuff.