Is varnish with a flash point above 40 celsius safe in a microwave oven? I've painted regular white mugs and want to varnish them too. 
But my varnish has the following specs:

Gloss varnish based on alkyd resin.

Flash point: Above 40 degrees celsius. 

Is it safe to varnish on some sections of the painting on the outside of a mug? Or will it catch fire if microwaved to boil water or something?

I have no background in chemistry... took me a while searching around before I finally decided to just ask.
The flash point is for the solvent, i.e. for undried paint. Dried paint will have a considerably higher flash point, well over 100 degrees Celsius.

You should also consider toxicity. I don't think alkyd based varnish is approved for use in items you put in you mouth (like mugs).