That depends on the flashcart, some require to be able to read/write at a certain speed or you experience stop motion jerkyness when you play or during saving.
The thing about microSDHC is that, if there is no class number printed on it, it is defined as a class 2 the lowest read/write ability. Every class 4 I have has the class 4 logo on them. I have 5 class 2 and none of them have a class 2 logo printed on them, 3 of the 5 are from different vendors.
If your putting the flashcart in and it is not booting, that is more likely you didn't setup the firmware and flash the bootstrap (depending on what version you got).
If you got the OLD EZ-Flash V, it doesn't support microSDHC. In this case you would need to get an updated version which is the EZ-Flash Vi, which does support microSDHC.