If you have more than 1 professional killstreak set (say one for the market gardener and one for the rocket launcher) and you have 5 or more kills, will your eyes show 2 effects? Similarly will your weapons show 2 different effects as well?
You only see the eye effect when the professional killstreak weapon is out. However, all weapons with killstreaks active count towards your eye effect. This means if I got 10 kills with my killstreak rocket launcher (no sheen, no eyes, just killstreak), then switch to my professional killstreak escape plan, you see the eye effect until I put my escape plan away.
The killstreak counter in the kill feed is based on that specific weapon, while the killstreak on your HUD is everything combined (all killstreak weapons; non killstreak weapons do not add to it). The sheen frequency and eye effect use the combined killstreak, meaning sheen frequency also carries over to other weapons, if you have multiple specialized killstreak weapons.
If you have multiple professional killstreak weapons with 5+ kills, switching between weapons simply swaps the eye effect according to the active weapon and its associated effect. They most definitely don't stack.