If it is in air, GC-MS would be more appropriate since dioxins are volatile compound. I'm no expert to this kind of environmental testing (e.g. air testing), but in order to test in air you will need some kind of filter (e.g. carbon filter) to capture ambiant air contaminant. The problem I see is more around the capture protocol, you will have to make sure that a fixed amount of air goes through the filter. Then organic extraction should be performed on the filter before GC-MS (standard procedure to do so should be easily found by googling). Most people who test for Dioxins test exposure instead of air level. They test tissues, plasma accumulation. 

There are no useful approaches to dioxin (PCDD/F) analysis on LC-MSMS. The main issue is that the separation of the (2378 and non 2378) congeners with their individual TEFs (Toxic equivalency factors) is only possible on a GC column.

There are approaches for the analysis with triple quads (e.g. the TSQ Quantum XLS Ultra)  instead of the usually used sector field instruments but they are also in combination with GC (see Thermo Application Note: 52266).

For cleanup you may have a look at ISO 16000-13 and ISO 16000-14, but again You will need a GC instead of LC.

+1 for both of the previous answers. I would add that we have successfully run ambient air samples using polyurethane foam. About 16hours at 1m3 per minute. Check out some of my publications, most are for download on research gate cheers Robert

+2 for all the answers above - as well as the resolution issue for the 2,3,7,8's there is the issue of sensitivity as well - I am not aware of any current triple quad MS systems with the sensitivity to do PCDD/Fs at ppt levels - may be possible on new orbitrap systems ?? not sure but may try it soon

Normally for separation of all the isomers of Dioxins,Magnetic Sector GCMS (HRMS) is recommended. But now a Triple Quadrupole GCMS can also be used for Dioxin analysis with fairly good sensitivity. The most crucial part will be the sample collection / preparation.

The polyurathane foam PUF is good to sample the lighter chlorinated congeners. However Another filter should be used to trap the higher chlorinated congeners since they are more likely to be associated with particles. Glass fiber filter is good for that. There are a bunch of publications on that matter (Broman et al and Näf et al).