Training as a martial artist -- or really, any athlete -- is so different from training to look or feel good. Flexibility, freeweight exercises, the olympic lifts, old time lifts, strongman competition events, powerlifting techniques, mobility training, agility, and a hell of a lot of attention paid to recovery all suddenly become important.
Flexibility is important, but mobility is where it's at. Think of being flexible as having a huge power amp, and great mobility is a 4x12 cab. Mobility is the ability to move a joint through a large ROM
without external pressure, like being able to to bring your knee to your chest without bending your back or using your arms. Low flexibility puts a ceiling effect on mobility, limiting its progress. FWIW, standing yoga positions have helped with my lower body mobility a lot.
Also,
this article is long but it will make all the difference in your progress.
EDIT: I train MT and boxing, and when available bjj. Can't afford membership right now so sparring and hitting pads with my more mma-trained roommate, next semester starting with the university wrestling team and bjj club. Heading to my 2nd free sanshou class tonight, it's cool but too expensive and similar to MT so I won't be training it regularly unless I have several sudden windfalls of cash before March

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