Hi friends
I hope that both of you are correct. But only the conditions are different.
For the same flow, as in the case of venturimeter, when the cross sectional area is reduced, the velocity( or dynamic pressure) will increase and the static prssure exerted on the side walls will be reduced
For the same cross sectional area like ther tip area in the burner nozzle, when the static pressure is increased by means of increasing the primary air fan speed, both the velocity(or dynamic pressure) as well as the flow will be increased.
Regards
Vinayak