I'm actually not sure it's a hip flexor. I just know that normally this time on Sunday I'd be out on a 30 mile ride and instead I'm sitting on a bag of ice. It's been bugging me for a while so I've decided to shut it down until I see a doctor.
Meantime, how can I maintain some semblance of cardiovascular conditioning? It's taken me a long time and a lot of work to get in my current shape and I don't want to start all over again whenever I get back on the bike.
I've strained hip flexors twice. Give it a few days off, with lots of ice.
Then maybe you can try some easy riding. Because offhand I can't think of any cardio exercises easier on a hip flexor than cycling, with it's limited range of motion and lack of sudden explosive movements (unless you want them).
A stationary bike or trainer would probably be best.