Flax oil and linseed oil both come from the same plant. Thus, it will be compatible with any finish that is compatible with linseed oil. The only difference is that flax seed oil is cold pressed and linseed oil is processed by pressing, heating, and using petroleum based chemicals to increase the yield. Either raw linseed oil or flax seed oil can retard the drying of a finish applied over them because they do not have chemical dryers added to them as boiled linseed oil does. However, both flax seed oil and linseed oil will polymerize or harden over time. This is why the traditional English Oil Finishing processes can take months to complete if done properly, although some folks will add chemical dryers to speed things up a bit. Flax seed oil is a food grade product, more pure and safe for human consumption. But flax seed oil does not have as good a shelf life and should be kept refrigerated. Thus, anyone who uses flax seed oil as a solvent carrier for alkanet dye would do best to only produce small batches. I didn't know that until after I bought it.
I confess that I've never tried doing a traditional English Oil Finish as damascus has posted here in the Double Gun FAQ forum. You should read his thread because it has a lot of very good information. I'd like to give it a try because I was very surprised when I did a little experiment a few years ago. I applied a couple coats of several different clear wood finishes to the same piece of planed black walnut to see how they either covered or accentuated a glue joint. The degree of difference was amazing.