There is no such thing as "Flywire bank transfers". They are a financial services company, not a bank.
Flywire probably has accounts with banks in multiple nations, so that they can offer regular SEPA instant transfers (that are already supported by bunq, even though for some reason they aren't listed there) as well as some national instant transfer schemes, enabling them to transfer money fast even in situations where the two banks don't have support for the same scheme.
As for the Dutch scheme, bunq could opt to support the Dutch national scheme in addition to regular SEPA instant transfers, but that would mostly help Dutch customers only and will become irrelevant when more Dutch banks join the ECB's standard. They still wouldn't be able to offer national instant transfer schemes of other countries anyway and strategically it's probably also a bad call, as users would benefit from EU-wide standardization more than on a regional scale.