I've been using BLO for years. I love the way it smells and what it does on wood furniture I've made. I've never tried using Raw Linseed Oil (RLO a.k.a. Filtered flaxseed oil w/ no additives) but I've heard rumors about how it color shifts faster due to having fatty acids or some such that BLO doesn't have. I saw a bottle of this stuff at whole foods so I grabbed one and figured I'd give it a shot. Across the internet I've found people saying "weeks" to "months" to "years" for the color shift to occur. I do have a few rifle stocks (non-US rifle) that have BLO rubbed on them for 10ish years now. None of them really have changed color to a reddish hue so I'm inclined to believe the comments of, "BLO won't cause a reddish hue."
The stock I'm using it on is a refurb replacement scant 03A3 drill rifle stock that I stripped the varnish finish off of as best I could (some tiny patches remain - it's a bitch to get that crap off). It had one coat of BLO rubbed in sometime last summer and is obviously pretty dry. I honestly couldn't tell much of a difference in the application of the oil it soaked in, and when I came back an hour or more later it was more or less completely "dry". By "dry" I mean when I went to buff the excess off the surface there was almost none left or transferred to a clean paper towel.
I'm planning on sticking to the mantra of once a day for a week, once a week for a month, and once a month for the rest of your life at a minimum. I might do a few coats in a day depending on how the wood reacts to soaking up the oil. It's pretty dry here in Colorado so the wood may be "thirstier" than in other places.
Original before stripping the "parade gloss" varnish
1 coat BLO 1 coat RLO
and a comparison to another drill rifle stock that I have not yet touched. You can see it's dirty, dry, but the original reddish hue is intact. I'll probably just use denatured alcohol to clean some of the surface dirt off then go straight to oil on it. You
CAN just go straight to oil, and it will remove the dirt, but why not clean it first if you can do it fairly quickly.
I'll probably not update the OP, but rather just reply with new pics/updates, as I add additional coats of oil. I'll start taking the pics in a more controlled environment so the color shift will be more easily noticed. Probably on my workbench in the garage or the concrete patio in my back yard.