I have a flashing glow plug light and my car smells of burning

Get it to a good mechanic as soon as you can! An electrical smell AND smoke means a serious electrical short. Glow plugs use very high voltage so you risk a possible fire. There being no light means there could be a problem somewhere else in the system as well.

Make sure it is a green brake light switch.

Your glow plug light is fed from your glow plug circuit , a problem on that circuit would flag up a flashing light

The obd light with tell specifically what it is, is it gas or rotten egg - the latter means catalytic converter, gas smell probably flooded or not firing on one or more cylinders, need more details. Also, if the light is flashing it's warning of catalytic damage - raw fuel hitting the cat, smell could be heat from cat trying to burn off raw fuel,it will glow red hot.

the glow plug are used to heat the fuel on start up only, as a diesel uses compression instead of a spark (from the spark plug) have you try checking the connection on the glow plug, or changing the glow plugs themselves?

Classic 109 relay failure.

Relay is for the Glow Plug system.

This relay provides the power to all of a TDI's engine-based electronics.

If the glow plug light comes on intermittently by itself, check your brake lights too.

A burned-out bulb will cause the glow plug indicator light to come on. Sometimes flashing is caused by a bad Brake Lamp Switch on the Brake Pedal. It was updated for free by VW .

If you can see it under the knee panel, the Brake Lamp Switch body should be Metallic Green....if it is Purple or Black it need updated.

this means that u have one or more burned out glow plugs

sounds like a glow pug fault.it will flash if one glow plug has a fault.

Despite what you may read from other comments....The glow plug light is simple a multi function warning light and IS among many othed things in fact used to warn of brake light and brake light switch failure. Therefore it can NOT be treated as glow plug problems only.
I have worked on V.W for many years and have encountered this problem many times. You should get the OBD codes read. This will reveal the exact problem...and there may be more than one
You can contact your V,W agents if you wish and check to see if I am correct.
Best of luck
John

light come on or flashing