Center brake light flashes along with right blinker only

Replace your brake switch on the pedal. If problem continues you have a bad ground somewhere

bad bulb on right side check and replace

Sounds like a bad ground connection, probably in the back. You'll need to find the bad connection. Or if you can figure out which wire is the ground wire, connect it via a new ground wire to the body.

Usually a fast flashing signal is because one of the bulbs is burned out or shorted out. If the signal and brakes use the same light which many cars do then check the wiring to it and replace bulb. If burns out again then it has a short between the signal switch and the actual light or the brake wiring to it is shorted.

It sounds like a bad light socket. The brake light and the parking/running/regular part of the socket are shorting out. When you press on the brake petal it's shorting out on the turn signal and sending current to the indicator (arrow) on the dash.. When you use the blinker, it's shorting with the brake light and causing them both to flash...

Check the socket and get back to me with the result.

You will need to replace the rear light assembly that was melted.

you have a ground fault somewhere, try cleaning all the ground leads look for corrosion and rust.

THIS PROBLEM MAY BE A DEFECTIVE TURN SIGNAL SWITCH OR A DEFECTIVE BRAKE LIGHT GROUND, THE BRAKE LIGHTS ARE GROUNDED NEAR THE SOCKETS, YOU WILL NEED TO PULL THE TAIL LIGHT ASSMEBLIES OUT TO CHECK THESE GROUNDS TO THE SHEET METAL.

you have a back break light out

I can't look up your wiring diagram because I don't know model year?
On some makes and models, the lower brake lites are wired through the multifunction switch. Your turn and stop use the same bulb filament, just not at the same time. On a left turn, the left turn signal works, but the brake lite on the left doesn't. Now, the brake lamp on the right does work. The high mount brake lite also will work. The highmount brake lite is usually wired differently than the lower brake lites.
W/o being able to look at wiring diagram, I don't know if my info is applicable on your vehicle? I need model year.