Why don't you call flyby and ask them? If it's on a single ticket they likely will through check, if it's not - they might.
A lot of airlines won't on two tickets because the MITA (IATA's multilateral interline ticketing agreement) doesn't apply. This agreement sets out procedures and liability in case the bag gets delayed or lost.
Some airlines will do it on-line, or intra-alliance (BA, for example) but check their conditions of carriage before you go to the airport.