I'd add that with that LP (low profile) chain, the max bar size is really more like 20". I think bailey's revised their maximum bar recommendation. I tried it on a 32", then a 20" bar with my 394XP, but it was just too powerful. It literally pulls it apart. On bigger bars, it slaps around quite a bit, and stretches quite a bit. If you already have a 20" bar, which is pretty standard for saws that size, you can mill with that. Sometimes those saws will use .325 chain, which there is also milling versions available for, but they have a wider kerf, and therefore use more energy to run. If your bars have replaceable tips, you can save money by just converting them (or getting your local saw-shop to do it for you) to .375 from .325. You'll have to replace the rim sprocket or spur sprocket depending on which type those saws use with the appropriate .375 sprocket. The LP chain really uses MUCH less power to drive. In a pinch when I'd broken the starter cord on my 394 up in the woods, I milled a bit of cherry with a 361, which is a little bigger than what you have, but not by much. It still went pretty fast on 15" dia. logs.
One key I think with using smaller saws, since they're going to be running at wide open throttle for much longer per cut, is to increase the oil mix ratio a bit, like maybe 40:1 or even 35:1 instead of 50:1 to ensure that the saw is getting proper lubrication, and maybe letting it cool a bit for a few minutes or more after each cut. Just take it easy; keep the depth rakers lower than you would with a chain for normal woodcutting, and slide the saw slowly into the log. Let the chain do the work. Its going to make tiny powdery chips no matter how big the saw and no matter how big the log. Remember you're cutting into end grain the entire way up the log. Also, as Aggie has posted in timing tests, an angle of about 15deg. makes a faster cut than 5-10 deg, although its a little rougher cut. This shouldn't matter at all on posts.
Needless to say, you need to make sure that your oiler is up to the task. With the LP chain, it should be a little easier, but if they are adjustable, make sure they are on maximum oiling.
I personally use canola oil for milling; you can find information about it here. I've used it since I got the saw a couple years ago, and have found no problems whatsoever. Some people don't like the idea of using a veggie based product; its up to you, its just that I can use the sawdust on the garden afterwards, and canola is actually viscous to a lower temperature than petroleum oil. Corn oil freezes, however. As long as you don't leave it in the saw for a long time, it doesn't gum up at all.
