The blinkers in my '92 Buick park avenue ultra

You'll need to inspect each bulb to see if it is getting power.
Front and rear.

take a screwdriver and hit the MAF sensor lightly . if it stall the MAF sensor is defect.

Cant say for sure, but you may be laying something on the sensor that turns the lights on, and causing car to think its night time, and turning on lights. The sensor that controls this is on dash ,drivers side near windsheild.

Does the front and rear light on the right side come on when you activate the switch ?
If a light is out the system won't flash.
If one side comes on and the other does not, the problem is usually in the turn signal switch.

If the light is on the engine computer will have a trouble code or codes, which may help you towards solving the problem. Have the computer scanned for the codes. Go from there. Good luck.

Check your drivers side front CV joints and make sure the dust covers aren't ripped or broken. You;ll also want to check to make sure part of your splash guard isn't rubbing against your tire.

what relay are you looking for there are some under the hood on the passegers side firewall and then some on the passengers side under the dash behind the kick panel

I have a 98 Bucik Park Avenue. I recently had it painted and when the body man put the lights back in I began having problems with the brake lights and turn signal lights. Only one brake light lights up and only on signal light lightsup and they are on opposite sides. I have changed the bulbs (all) and I have tested the fuses(All).

If the lights are coming on, but they won't blink, it could be the turn flasher relay.

Check your flasher unit.