My kitchen sink drain, which is tied into the main sewer line outside of the house makes a gurgling sound when the toilets are flushed and sometimes the sound occurs without the toilets being flushed. This all started after I installed a new flush valve in one of the toilets.I think that the gurgling sound may have something with the venting of the main sewer line which comes out on the roof. If this is the problem, how do I unclog the vent pipe??

You need to safely climb onto the roof and rod down roof to basement floor plus about 15'using a 1/2 or larger rod.