The conjecture about 233-flows, stated in the last section in openproblemgarden text is already false for Petersen graph (234-flows also don't exist for Petersen graph).
Looks like there do exist 333-flows and 244-flows for all snarks (verified for all snarks with 10, 18, 20, 22, 24, 26 vertices).
Also looks like almost all snarks have 233-flows. Here are the exceptions (5-edge connected snarks):
- 10 vertices: g1 (no 233- and no 234- flows)
- 18 vertices: none
- 20 vertices: g1 (no 233- and no 234- flows)
- 22 vertices: g6 (no 233-flows)
- 24 vertices: g7, g12, g26, g29 (no 233-flows)
- 26 vertices: g62, g67, g88, g89, g93, g98, g109, g119, g138, g143, g166, g177, g189, g191, g203, g246, g277 (no 233-flows); g141 (no 233- and no 234- flows)