Furnace squealing is almost always due to motor spindle either dry or bent (or both.) Although it could just be a loose screw on the sheetmetal somewhere and squeaks from the vibration. The furnace itself is a pretty simple unit. If you're reasonably handy you can probably do the whole job in about 3 beers. Take it all apart, if the motor is the type you can separate from the case, then clean and lube the spindle with dielectric grease, all other moving parts (hamster wheel) with dry graphite, and reassemble while snugging up all the other screws, paying extra special attention to the motor mount. If you determine the motor to be the culprit they run about 90 dollars direct from Atwood (YMMV depending on part #) but at least you'll be comfortable doing the job because you've already had the unit apart once. Also be sure to check the hamster wheel for roundness and the motor spindle to make sure it's not bent even a little. If they are, you must replace or the problem will never go away.
Also FYI you really need to order the motor by the part number stamped on it or on the sticker, not by the furnace's model number. They change the impedance and winding and all sorts of stuff all the time with really no rhyme or reason and the wrong motor will smoke your board pretty quickly.
By the way here's your service manual: http://bryantrv.com/docs2/docs/hflamefurn04.pdf