I am not quite sure that if I don't deactivate trypsin what is going to happen to the cell suspenssion. Apart from serum which is being suggested for deactivation, what else could be used for this purpose?
As long as you are using at least 1:1 ratio of 5-10% serum-containing medium with your trypsin there should be more than sufficient inhibition, followed by centrifugation and medium exchange with fresh medium.
If you want an additional chemical, we have using Defined Trypsin Inhibitor for some experiments. There are more here:
Your complete media contains FBS or FCS, it acts as a trypsin inhibitor. No need to use separate one. Otherwise after flushing just go for centrifugation and remove the trypsin and add the media into falcon and pour in flask which already contain media.