I am having this exact same issue with the P-51 and Vaicom Pro. It affects only the P-51, and not just in the Blue-Nosed Bastards of Bodney campaign, it's in every mission you might fly with the P-51 module.
I can, in the same session, fly the F/A-18C and Vaicom works flawlessly. When in the P-51, commands are only instantaneous while on the ground, once airborne, they are massively delayed. Even saying "options" to bring up the on-screen menu will sometimes take upwards of 2 minutes to appear, whereby I will usually just fumble for the F-keys to select commands instead of waiting for Vaicom to send them to the sim. The commands are sent instantly when doing so, it's something about the interface between Vaicom and comms with the P-51 module that appears to be borked.
To be fair, I can't be sure it has ever worked myself, as I started flying the P-51 a couple weeks ago, and I installed/purchased Vaicom in May of this year. I am fairly new to DCS (since April), but I'm reasonably sure my install is correct and my configuration in Vaicom is working, as evidenced by the perfect functionality in other DCS modules/campaigns/missions.
I'm using the Steam version of DCS on the openbeta branch.
EDIT: You can see in VoiceAttack that the commands are registered and ostensibly being sent, and they do eventually reach DCS and are interpreted, just after a very significant delay.