As someone with super tight hip flexors I get the struggle! The challenge is exactly what you said, the sitting all day thing shortens and tightens them soooo much and then add in running. First I’d do some very gentle stretching before and after running, you can do deeper stretches after running. However, only light mobility before as stretching fatigues muscles.
Here’s a video with two of may favorite stretches: the first and last in the video. You can fast forward to minute one and skip the intro blah blah section ( ;
The second stretch of the series is a good one too however it can be quite challenging to do well for individuals with really tight hip flexors and can put a lot of strain on the low back if not done well.
Next, if I have a big day planned on my computer I switch from sitting to standing every 30 – 60 min and I set an alarm for every two hours and get up and move around. Even easy walking can help loosen hip flexors a bit during the day. If you can get a stretch in multiple times during the day great though I realize certain work situations are conducive to that.
Last but not least. I’m not sure how old you are, I am 53. I’ve noticed over the years it takes more and more work to stay mobile (yay menopause and aging – haha) and that heat really really helps me. So I have a microwaveable rice filled hot pack that’s a big rectangle and fairly heavy. I’ll heat that up and do stretch #1 in the video with the rice pack on my hip flexor area and that really does the trick for me. You could also use a heating pad, I like the rice pack because it’s heavy and stays put.
Good luck with the hip flexors and I hope this helps ( :