How can I remove a flag in C?

Short Answer

You want to do an Bitwise AND operation on the current value with a Bitwise NOT operation of the flag you want to unset. A Bitwise NOT inverts every bit (i.e. 0 => 1, 1 => 0).

flags = flags & ~MASK; or flags &= ~MASK;.

Long Answer

ENABLE_WALK  = 0    // 00000000
ENABLE_RUN   = 1    // 00000001
ENABLE_SHOOT = 2    // 00000010
ENABLE_SHOOTRUN = 3 // 00000011

value  = ENABLE_RUN     // 00000001
value |= ENABLE_SHOOT   // 00000011 or same as ENABLE_SHOOTRUN

When you perform a Bitwise AND with Bitwise NOT of the value you want unset.

value = value & ~ENABLE_SHOOT // 00000001

you are actually doing:

      0 0 0 0 0 0 1 1     (current value)
   &  1 1 1 1 1 1 0 1     (~ENABLE_SHOOT)
      ---------------
      0 0 0 0 0 0 0 1     (result)