Go get a drill bit and chuck it into your drill and pull the trigger. Look straight on at the end of the bit while its spinning and take note the perceived size of the spinning bit. Now repeat the exercise, but chuck the bit very slightly off center. Note that while spinning, you essentially have a larger diameter. This is precisely the situation with your shaft. Its slightly off center, and when it spins it will "expand" in size. That perceived expansion will cause a leak in your packing, because it represents a gap. That's why shaft alignment is so important, because it's the only real way to make your packing really work well and run cool.
So do this. Go stuff your packing gland. Don't get it too tight as it's rather difficult to loosen up packing once it's been compacted. Just backing off the nut won't do it, so just avoid getting it too tight to begin with. If your packing rings are the right size but too thick to easily go into the gland, a trick is to gently flatten them ever so slightly with a hammer. When you put your gland on, tighten it to hand tight and go maybe a quarter turn more. If not a nut type gland, basically just seat the packing without compacting it. If the boat is not in the water, launch.
At rest in the water, tighten the gland until it just stops dripping, then just a bit more. You can go run the boat and seat the packing in a bit, and observe the drip rate when running. Once the shaft stops turning you should have little drippage that goes to nothing after the shaft sits for awhile and the packing expands. Basically after a hour it should have no dripping.
You have just adjusted your packing in a perfect world. Because in a perfect world, our shaft alignment is perfect. In reality, you likely see some water dripping, flinging, or even gushing when running. This will be exactly proportional to the quality of your entire running gear in concert with each other and it is the state of your running gear that will ultimately determine how your packing gland will respond next and whether you will be successful.
Ideally when running you want about a drip or two every minute to lubricate the packing for flax packing.dripless packing does not need it. You don't have to have the shaft spinning when you check as it will take a few minutes for packing to expand after you stop running, so you have time to check. Just tighten the gland, no more than about a quarter turn a time as you get close. If you have good shaft alignment, you will be done almost immediately. If not, put your hand on the shaft each time and the bad news is that the gland will get too hot before you eliminate the excess leakage. Stop before you score the shaft. Packing glands just won't fix alignment issues. Most of use will be somewhere in the middle with little to no leakage and acceptable gland temps. If you can't comfortably hold it, it's too hot.