They did.

In the very first pilot episode, The Gathering, Sinclair and Garibaldi suit up in black padded vests when going after the changeling net assassin. Garibaldi takes a PPG hit directly to the chest during the fight, which throws him backwards harshly, but otherwise he's unhurt. He hurriedly sheds the vest, because it's now on fire from the blast, and comments he's fine, armor got it.

You see these black vests and variants of them on and off throughout the series, usually only when security is expecting heavy return fire and they have time to set up with them.

They did.

In the very first pilot episode, The Gathering, Sinclair and Garibaldi suit up in black padded vests when going after the changeling net assassin. Garibaldi takes a PPG hit directly to the chest during the fight, which throws him backwards harshly, but otherwise he's unhurt. He hurriedly sheds the vest, because it's now on fire from the blast, and comments he's fine, armor got it.

You see these black vests and variants of them on and off throughout the series, usually only when security is expecting heavy return fire and they have time to set up with them.

If the question is more about why aren't people seen in armor all the time, well, in addition to all the reasons noted in comments (protection vs mobility, intimidation factor), constantly marching around in riot gear like you're about to be shot sets a very bad expectation of success for your space station dedicated to peace and trade.