2008 Chevy Silverado Signal lights work in the back but not the front

Do you tow a trailer? If so check the trailer light plug to see if any of the wires are touching.

change the front bulb

I would try measuring for 12 volts at the socket while the turn signal is on.

you need a new horn, and find the bulb that is out

Then you need someone who can,like a repair shop

Bad bulb left rear.

No - headlight ok.
The reason that the Right turn signal blinks fast is that there is half the normal load (resistance)
on the right side, since the Right front turn signal isn't working.
Since you replaced the Right front turn signal bulb, your problem lies in the bulb socket or
the wiring to the socket.
(1) try cleaning out the socket - there's probably a contact problem in the socket. You
may need to squeeze the contacts together to provide good contact to the socket contact.
(2) if contacts inside the socket are ok, try back-probing the socket - to make sure that the
socket is getting 12V DC to light the bulb. Replacing a bulb socket is easy, and commonly done.
Any auto parts dtore should be able to sell you a new socket - its just a matter of cutting out the
old one, and then splicing in the new one. Most shops will use small wire nuts, buried under several
wraps of E-tape (electrical tape).
(3) if bulb AND socket ok, you have the worst problem known to man - a wiring fault. In this case,
you'll want to run a new wire from the flasher module (under the dashboard) to the turn signal.

you have a bad ground to the taillights , the signal is looping back to the front light grounds

I think there is a wiring connector in the harness that may be loose or corroded. Trace wires from back to front.