Can flint be obtained from gravel that a player placed when it is mined?

Yes, you can get flint from it even if you placed it. Flint has a small random chance of dropping. If you mine the block with fortune enchantment, it will be more likely to drop flint. If you use a tool with maximum fortune level of III (3), it will have a 100% chance of dropping flint--i.e., it will always drop flint. If you use a tool with silk touch enchantment, it will NEVER drop flint. You may have been using silk if you are having 0 luck with it.

Yes, you can get flint from gravel you placed yourself.

Given a 10% chance to drop flint, you have a 0.515% chance to not get any flint after mining 50 gravel - [(1-0.1)^50]*100. You might have just gotten really unlucky. Or, a mod on your server might have affected your ability to get some (though you say this was replicated in smp, so probably not that)