If I pay up front for flights and hotels for my family's holiday abroad (so I snag the credit card miles), and they transfer that money back to my bank in SG, are those inward funds taxable as income?

No, inward fund transfers are not considered as income, so it is not eligible for tax

Hello. The definition of income, as I understand, is "money received, especially on a regular basis, for work or through investments". As you did not "earn" the money (it's a reimbursement), it does not constitute as income.