Hi Andrew.
The code is in the "beta" branch in github:
you can see the code at the bottom for the LLLWalk algorithm.
It only does one (possible) flip per step, using a counter iLLLWalkClausePosition to keep track of which var in the clause to potentially flip... when that's zero, it selects a new unsat clause.
Introducing the multiple flips per "step" may break other components (caching which clauses are currently unsat, etc.)
For convenience, I would recommend you do something similar to what LLLWalk does for your project. You could determine all at once which vars to flip and store them in an array, but then just spread those flips out over several steps.
What we could do is add a new "real step" statistic [or something like that] so you could collect the data and distinguish between "flips" and "steps" in your stats.
let me know if you need any additional help.
-Dave