Milam glacier falls under the Nanda Devi Biosphere Reserve limits. In case you want to enter a national park limits, you will need a permit from the forest department. Additionally, since parts of NDBR fall under the protected areas act, you'll need a protected areas permit to enter the national parkMilam glacier section. The permit to enter thisPAP can be obtained from the forest department in Joshimath orMHA, Dehradun. The other option is to contact themthe forest department of Uttrakhand and see if you can get the permit from some other source. In caseIdeally only a PAP should cover both the protected areas permit and the forest department ispermit. If not empowered for a PAP, you'll have to contact the MHA (Ministry of Home Affairs) foradditionally get the same (the forest department will give you the information for this)permit from Joshimath or Dehradun.
Most of the national parks in India mandate a guide as this would prevent the tourists/trekkers from wandering off the set trails. I do not see why this would be any different in NDBR (Nanda Devi Biosphere Reserve) as this is a UNESCO world heritage site. Most of the guides for the NDBR are located in Joshimath.
The other option is to directly contact a trekking agency in Joshimath and allow them to arrange for both the guides and the permit for you.
Also, please note that the national park is open only between May and October.