I have squeaky front wheels. Sounds like a hamster wheel. No change during braking. I jacked it and the classic wheel bearing rock test had slight play. I tightened my drivers side wheel bearing spindle nut and that squeak went away. I'll do the same on the passenger side.
The 1980 Buick Chassis Service Manual published by GM says this about adjusting it:
3. Tighten the spindle nut to 16 N*m (12 ft. lbs.) while turning the wheel assembly forward by hand to fully seat the bearings. This will remove any grease or burrs which could cause excessive wheel bearing play later. (Figure 3C-2)
4. Back off the nut to the "just loose" position.
5. Hand tighten the spindle nut. Loosen spindle nut until either hole in the spindle lines up with a slot in the nut. (Not more than 1/2 flat).
6. Install new cotter pin. Bend the ends of the cotter pin against nut. Cut off extra length to ensure ends will not interfere with the dust cap.
7. Measure the looseness in the hub assembly. There will be from .03 to .13mm (.001 to .005 inches) end play when properly adjusted.
That play and squeak was less than a year after it was adjusted per the manual. This time I turned it tighter instead of looser but I failed to keep track of exactly how much I turned it. I don't think it was more than 1.5 flats.
I used a scale-type torque wrench to try to gauge just how tight it was. The one I have is craptastic. I can at least tell you it was somewhere between 5 and 20 ft-lb. Am I gonna burn up my wheel bearing? The wheel does not fail the rock test anymore, and spins freely.
You might be able to silence it with some silicone caulk. I took my wheelcovers off, planning to caulk them, then got lazy and drove around a while without them until I scored a set of '57 Buick Roadmaster wheelcovers that look surprisingly nice on my car, but then one of those keeps flying off so I'm driving around with 3 installed and one stored until I do something about that....at this point it's only a month until I'll be putting on my winter tires which are on aluminum wheels anyway...