Hi, this track hub is hosted at WashU. If you click on the track itself on the UCSC genome browser you will be taking to http://goo.gl/X9pVFg. At the bottom of it, there is Ting Wang's email address for further contact. Perhaps they would be able to help downloading the bed files?
To access the files you are seeing displayed in the browser, you can navigate their public hub's directories and find the trackDb file that points via "bigDataUrl" statements to the location of each file displayed. Below are some short scripts you can put on the command line that will pull out those statements and create links via the relative location of the defined files. First obtains the URLs of all the files, followed by just the .bigBed and .bb files, however, not filtered for only the ChromHMM track.
curl -silent http://vizhub.wustl.edu/VizHub/hg19/trackDb_dli_edacc8_new4.txt | grep bigDataUrl | sed -e 's#^.*bigDataUrl # http://vizhub.wustl.edu/VizHub/hg19/#'
curl -silent http://vizhub.wustl.edu/VizHub/hg19/trackDb_dli_edacc8_new4.txt | grep bigDataUrl | sed -e 's#^.*bigDataUrl #http://vizhub.wustl.edu/VizHub/hg19/#' | grep 'bb\|bigBed'
These are the binary bigBed files that can be turned into bed files with the bigBedToBed utility located in the appropriate directory here: http://hgdownload.soe.ucsc.edu/admin/exe/
Another approach is to use our Table Browser. With the hub data displayed in the browser, click the top "Tools" button and navigate to the Table Browser and then set the group to "Roadmap Epigenomics Data Complete Collection at Wash U VizHub" and then select the "Roadmap ChromHMM" track at the very bottom of tracks. You could then choose each table and get the output from each track individually as bed files.
I suggest investigating the resources for accessing this externally hosted data (Public Track Hubs are not created or maintained by UCSC). You may also be interested in these tutorials about accessing Roadmap Epigenomics Data: http://www.genome.gov/27555330
I looked at this discussion before posting the question here actually. I tried searching for the URLs (bigDataUrl) for the files that I need, couldn't find any. Also emailed Ting Wang a couple of hours back. Waiting for his reply. Thanks anyway!