The method being used by schools like this is called "three-cueing", or "balanced literacy", or "Meaning-Structure-Visual (MSV)" reading! This method can also include "whole language" reading (also known as "whole word" or "look-say") programs that don't explicitly mention phonics. These programs often, but not always, also include phrases like "unstructured time" and "free choice".
There is no single program that's best for literacy teaching, but most states (and many parents) are recently turning to "science-backed literacy" or "science of reading" programs. These are evidence-based methods that target different ages and (dis)abilities in different ways to promote lasting literacy and critical thinking skills. Other similar programs are "phonics-based" and "structured literacy". A lot of these tactics actually emerged from teaching kids with dyslexia, and accept that literacy is not intuitive or fun to everyone.
All education red/green flags have to be prefaced with the facts that 1) every child is different, 2) student needs vary by age, and 3) the classroom is only one small part of their lives––home exposure to vocabulary, role models, and intrinsic motivation to read also play major roles. There are also many institutional barriers to access. Disclaimer done, green flags for literacy curricula include:
Small student : teacher ratios, ideally under 18:1 until high school age.
A school library, ideally with an ILL program, and a classroom-specific library.
Consideration of phonemic awareness, phonics, vocabulary, fluency, and comprehension.
Structured time, multisensory techniques, small group work and echo/choral reading, "refereading" (where the student takes the lead with close correction and rerouting), routine assessment (weekly quizzes, book reports, etc.), and a focus on generative writing at the same time as reading.
Free flow of reading work between home and school; i.e., homework assignments, vocabulary logs, book club check-ins, exploratory literacy work in the community.
Work set at the upper edge of the Common Core standards for the age-appropriate reading band (or some other skill-pushing tactic, such as using Wordly Wise books a year early).
Vocabulary-building homework that focuses on the sound or meaning of the words themselves, in addition to how they appear in context.
For English: some exposure to Latin, Greek, and/or Anglo-Saxon roots and affixes aimed at parsing words on the letter-level. This could be a good litmus test for 3rd grade and up; if a teacher looks at you like you're crazy for asking about this, then it's almost certainly a non-morphological MSV program.
A plan for handling students who are slower or faster than the class progression.
You could directly ask the teacher/administrator what students should do when they come across a word they don't know. Common answers include "skip it and come back later", "stop and look it up" (my favorite), or "assume meaning from context". This last one is three-cueing.
For more information, I suggest looking at the US Dep't of Education's What Works Clearinghouse Practice Guides. This ranks the scientific certainty of evidence-based literacy teaching practices. Anything with a "Tier 1 Strong" ranking is a green-flag in a school curriculum.
