why I do it is to empty the gall bladder keeps the bile from getting stagnant.I do it maybe one a week

My personal reasons :o)
I did my "juice fast" to jump start my bowel cleanse, and it was extremely successful in that respect...I guess weight loss/ketosis just wasn't a particular goal for me. (Although I believe both of those things occured!)
Ingesting no fats for a few days/weeks can lead to the build up of gallstones. (At least that's what I've read.) I didn't have time to Liver Flush at either end of my fast so I decided to play it safe I guess by continuing with my oil.
I have a condition that benefits greatly from my taking high quality fish oils and I was reluctant to stop taking them while fasting this time. Only difference was instead of taking the capsules I squeezed the oil onto a spoon and took them that way.
I intend to do a longer fast....I'm gearing up for it now and one aim of that is to improve the condition (inflammatory) that I requite the fish oils for. I had thought I might take the oils for the first week only this time (aiming to go 4 weeks plus). Then see what happens after that...

I certainly have read of people taking flaxseed oil while fasting. (Flaxseed oil is not my oil of choice because I'm of the understanding it requires protein to be properly absorbed, and that many people who are in the less than best of health cannot convert it properly anyway.)

...I'll see if I can find any links about oils while fasting. The possibilty that I wasn't truly fasting didn't bother me at all during my recent fast but it's something I want to look into further before beginning an extended fast...

Thanks for bringing up the question :o)