You are able to reload your weapon with magazines in a vest, chest rig, or inventory. Hit r to reload, it will begin reloading. If you have multiple mags in different places or different ammo types, it will give you an option to choose which one. After that, wait a second and it will give you an option where to store the magazine that was removed from the weapon. You can put it back into the vest, in you inventory, or drop it on the ground.
While reloading do not hit escape or try to do anything else as it will cancel your actions and time WILL have passed.
To manually put a magazine into or remove from a vest or something, you must activate the clothing item. If you take a magazine out manually, it will always go into your hand and you have to drop, wear, or store your weapon.