Since Zeagle seems to be away somewhere the past few weeks (I didn't get my question answered on this forum either) I'll try to answer some basics for you.
If you search "how to maintain your camera waterproof housing" - it will be maintained in about the same way. I am not familiar with the Zeagle strobe, so don't know about the specifics of it having a removable o-ring, but most are removable & replaceable on all of the equipment that I own. I totally replace my camera housing o-ring about every 2 years - flashlights, I haven't replaced any as yet but I personally don't use them as often as I use the camera.
This is how I maintain my o-rings:
Any equipment I take into salt water gets soaked in fresh water and I'll operate the buttons a couple of times as well to help dislodge any salt/dirt.
Take out and dry with cloth.
Open the housing and inspect O-ring. If I haven't opened it in a dirty environment or swam in a dirty environment and the o-ring & the groove it's in appears clean - I personally don't remove it every single time. They are tight - that's part of why they remain waterproof. There are little plastic o-ring remover tools available, some use a credit card, some pinch it up in their fingers. Don't use anything that could scratch it. Try not to stretch it too much. Inspect for any dirt or nicks/cuts. Rinse it off in clean water & put aside to dry. Clean groove it was sitting in with a Q-tip then follow up with a lint free cloth. Do the same to the opposing side of the equipment/housing groove. Slightly lube O-ring - you want it shiny looking but no excess - and reinsert it. Do final inspect before closing. Make sure it is clean & there is no lint/hair/whatever.
I'll dunk this in fresh water or the pool before taking back into the ocean just to be sure it's all ok & functioning as it should. Also, setting everything up the night before the next dive works best for me since I require a few cups of coffee in the mornings before I'm fully alert and I won't be rushing to catch the boat.
I store this without any batteries and often not fully tightened/closed - my feeling is why compress the o-ring unnecessarily if it is just being stored.