I hope I can help you here with this. There is an interaction between the fish oil pills and the coumadin; the fatty acids in the fish oil pills decrease blood clotting times as well, so together, fish oil and coumadin pills can dangerously impact your blood clotting abilities.
Here is some information on that: http://www.livestrong.com/article/420617-does-fish-oil-flaxseed-oil-mix-with-coumadin/
However, the website Rxlist does not specifically mention CLA and fatty acids on its monograph on coumadin in the section on drug interactions: http://www.rxlist.com/coumadin-drug/consumer-missed-dose.htm
I believe if you wish to take this, you should speak to your doctor regarding the risks and benefits. It may be that more frequent monitoring of your PT / INR levels might need to happen to make sure your clotting levels are not dangerously affected. This is not simply an OTC supplement that is safe and harmless in this instance, since there is this potential dangerous interaction, I can not recommend it safely...unless you consult with your covering doctors and they agree to it and the extra monitoring it seems to require.
I hope I was able to help, and I wish you the best of luck,
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