I believe this should be the right method. Monthly Installment will only change if (non-fixed rate loan) the BLR have movements and the bank will recalculate the montly installment so that the loan period will remain as the original loan period. (however some bank got policy where the monthly installment stays the same thus extending the loan tenure)

Putting extra money into the flexi account will reduce the outstanding principle used to calculate the daily interest resulting in less profit charge by the bank when installment is due.

ie:-

Outstanding Principle: 100k
Installment Amount: 1000
If the income earned for the month is 600, then 400 is for the principle paid.

If you put 50k into the flexi accounts:-
Outstanding Principle: 100k - 50k = 50k
Installment Amount: 1000 (remains unchanged)
Since outstanding principle is halved, lets just assume income earned is also halved so it will be 300 then principle paid for the month will be 700.