With a barrel You want to switch to a solid bung as soon as the wine is stable and in the barrel.
Ie if you are finnished primary & mlf ( either in or pre barrel) and you add so2 then you should put in a solid bung. Preferably a silicone bung to reduce wicking , and risk of oxidization and bacterial spoilage that can be a risk with a cork or wooden bung
Unlike a carboy A barrel develops a vacuum as the angels share develops , this can suck a wet airlock dry , the water may contain spoilage microbes . And the risk of oxidizing is high.
This vacuum counters atmospheric pressure in a stable (non fermenting) wine in a barrel.
A solid bung is best , and a dry fermrite type bung durring active ferments until the wine finnishes activity . A couple months past is ok but for long term a solid is best practice .
Visit any commercial winery to confirm , or just call any cooper and ask.
Call Vadai , they sell silicon bungs.
Gum rubber is also ok , most home winemaking shops would have these in many sizes
http://morewinemaking.com/public/pdf/wobcg.pdf more wines barrel guide