Myiasis is the invasion of host tissue, but is there active blood-feeding, or is there another source of nutrition for the maggots in order to develop through their instars
Myiasis is an infestation caused by larvae of Diptera Brachycera in humans or other living vertebrates. There are various types of myiasis: cutaneous, cavitary (gastro-intestinal, etc.) and, depending on the species that causes myasis and on its location, the feeding of the larva can be different: exudates from wounds and sores, secretions of natural cavities, content of the gastro-intestinal trait, etc. Therefore, clearly the blood is not the only possible food for the dipteran larvae infesting the body of humans or animals. Regards,
Some Calliphoridae species (genus Lucilia) are mostly necrophagous, but can also create cuticular myiasis on living animal or even humans. Lucilia cuprina is well known for strikes on sheep farms, as well as Lucilia caesar. But several case reports have also highligted human myiasis caused by L. sericata, a necrophagous species. Such cases mostly occurs on persons with strong health diseases such as diabete and poor heath conditions. In such cases, necrotic tissues are present in wounds and necrophagous larvae can feed on.
This ability of necrophagous larvae to feed and remove necrotic tissues on living person is use for care (maggot debridment therapy). A lot of studies on this topic can be found in the litterature.
Surprisingly obligate blood feeding seems to be rare in maggots of cycloraphan flies. Obvious exceptions are the piophilid Neottiophilum praeustum and also the larvae of calliphorids of the genus Protocalliphora whose maggots feed on blood of nestling birds (see http://www.entomologicafennica.org/Volume21/EF_21_2/7Janoskova.pdf for characterisation fo protocalliphorids). For a long time these flies were considered rare until investigations of the nests of altricial birds revealed that conventional catch methods for adults did not work for these species and that in fact they are quite abundant in many Palearctic habitats.
As Rinaldo and Damien say, the majority of myiasis causing maggots feed on connective tissues, tissue slough from necrotic breakdown, and in some cases other maggots as well. I am sure blood may be taken, especially by the invasive species rather than the primarily necrophorous, but overall that blood ingestion is largely accidental.
I am also sure there are groups of flies that are haematophagous, other than those I have mentioned above, of which I am unaware but this will give you something to work from.
After I sent my answer I came across the ResearchGate site of Terry Whitworth https://www.researchgate.net/profile/Terry_Whitworth. He has done a lot of work on haematophagous maggots of nestlings and has references attached to his publications of other species I had forgotten about such as Philornis downsi, the fly causing so many problems for Galapagos birds.
Thanks for all your help. It seems the consensus is that blood feeding in myiasis flies is accidental, except for some bird-feeding exceptions. Thank you for your examples and references. I have always been really interested in the blood-feeding behavior, and I'm thinking of writing a review paper after I defend my Ph.D. I'd be glad to continue to learn about other examples from you.