Depending on your needs, I would spend some time designing the experiment to select the perfect method.
What is your starting material?
Good quality DNA comes from fresh material (e.g. lab-reared flies are probably the best. See this article about storage condition of DNA and subsequent quality: https://nwcommons.nwciowa.edu/northwesternreview/vol1/iss1/12), whereas older material gives less and fragmented fragments (e.g. flies stored in old ethanol, museum-based specimens. See this article about genomic analysis from pinned insects: https://doi.org/10.1371/journal.pone.0161531).
What is your ultimate sequencing method (NGS)?
If you aim to obtain few genes and/or short reads (like Illumina, typically 150bp), then your extraction can follow a traditional method (i.e. with heavy fragmentation). If you aim for long reads (like PacBio/ONT, typically >1000bp), then your extraction should be tailored to avoid fragmentation (e.g. using wide-bore pipette tips)
Will you be pooling many flies into one sample or not?
If you aim to obtain information about whole-population, pooling tiny organisms into one tube for extraction will be easier to manipulate. If you want to gain insight at the individual level, then you will prefer to separate the individuals into a tube each. If they are tiny (D. melanogaster 2mm long), using plastics that retain as much DNA as possible (e.g. low binding properties of tubes) is worth it in the long term.
What are your assets for equipment, budget, time?
Some methods require many pieces of equipment, like a vacuum centrifuge concentrator or a DNA Size selection system. Some protocols are more reliable simply because they use a commercial kit from start to finish, which is often more expensive than a homemade protocol. Finally, some methods require many hours on the bench (e.g. overnight precipitation), whereas others are quicker. I would evaluate my priorities before settling on one protocol.
How will you assess the quality of the extraction?
For any next-generation sequencing, it is vital to obtain good quality extraction, as you mentioned. You can check the degradation by running a gel, the contamination with systems like Nanodrop, the concentration with Qubit fluorometer.
This quality check should be done right after the extraction (I usually write it on lab notebook and extraction tube). Storing DNA extractions can greatly affect the quality of the DNA. Depending on your next steps, it is worth thinking about storing conditions (see this article on freeze-thaw cycles for DNA extraction : doi 10.1089/bio.2011.0016).
I have used various methods to extract DNA from small insects, for genomic analyses, such as Phenol-Chloroform (followed by cleaning steps to remove salts) and commercial kits, such as DNeasy Blood and Tissue Kit (see this article on whole genome resequencing of Drosophila: doi 10.12688/f1000research.9912.3). You might want to test different procotols on one or two samples before making an informed choice on the method (see this review with many practical tips: Moreau, Corrie S. "A practical guide to DNA extraction, PCR, and gene-based DNA sequencing in insects." Halteres 5 (2014): 32-42).
thank-you for your comprehensive answer. We have 100 flies to be divided in 4 pools of 25 and will do pool seq using the Illumina platform for SNP analysis. We are thinking of snap freezing the 4 pools in N2 liquid because they have to be transported across two different cities. I will be doing the genomics and the crossings will be done in a separate university. I will try different methods as you suggested but probably the DNeasy blood and tissue kit would be easier.
Do you have additional recommendations regarding the homogenisation of the insects ?