Eman, as a martial artist (and as Danny as well as others can talk to), flexibility of all types and particularly hip flexion are important to me.
The goal for me was true flexibility, with strong bones and powerful muscles backing it up. The key to that even when my hips were healthy was patient, slow and purposeful progression.
The enemy to good flexibility in my opinion is rushing the muscles; the warning sign is pain.
You have an extra consideration as we all did who are further along. The bones need fixing first. The muscles have been insulted, but the frame underneath needs to be solid. That solidity comes after six months, so to my mind, serious flexibility comes after that.
Despite long years of good flexibility, the OA had stolen so much of it that by the time of the surgeries, I not only had to overcome the impact of the surgery, but also the twisting and atrophy of muscles in reaction to the assault on my body.
So to reach the type (maybe not the extent) of flexibility that I had before was a long term project. My target was fourteen months. For no real reason, but it just sounded right to me. Not the kind of flexibility normal to most people, but a reasonable martial artist's flexibility.
I reached it at about that tme, not necessarily because that's what it takes, but probably because I paced it to that extent. It gave me confidence that I needed that my hips would support that for a long long time.
Knees to the chest, with work done both with at home and outpatient physical therapy didn't come for me until about five months. I slowly worked on it, stopping at the first sign of resistance and holding it at that limit. Never to pain.
Now, at almost three years, I am very flexible, can do every kick that I want not just in the air, but at full impact on a heavy bag. So for me, slow progression with as many exercises for strengthening both the large and small supporting muscles were important. I now mix weight lifting and yoga, sometimes in the same workout.
Long answer, but I feel strongly that flexibility is important to address patiently.