It would be useful to receive information on the dosage of specific compounds (C18:3n3, DHA, EPA, CLA, etc.) as well of their source (lineseed and others)
I think that you can find your response in attached paper. It should be noticed there is no information about daily requirement of essential fatty acids (18:2+18:3 and Omega-3) in Ruminants. For example, recommendation for linseed inclusion to diet (for improving reproduction performance or modifying milk FA) is up to 10% of DM (you can refer to Petit et al., 2010- Canadian Journal of Animal Science). of course there are a lot of papers and experiments in the case of unsaturated fat supplements and milk fatty acid profile, however, we should know the production of a high quality milk (rich in special FA) is not similar to essential FA supply and their metabolism in body.
In the case of interactions between CLA supplementation and reproduction in dairy cows, the results are inconsistent. and you can not find a common recommendation in order to promote reproduction or BW changes and etc when cows fed a CLA supplementation.
In fact effective dosage for omega-3, omega-6 and CLA is related to lactation stage and ration components (forage:concentrate, starch level, particle size and peNDF , etc), although physiological stage is determining addition of omega-3 or omega-6 to dairy cow diet (for instance, omega-6 sources from parturition until 60 DIM and Omega-3 from first service because of improve pregnancy outcomes at first service).