Does a family trust pay tax on capital gains it flows out to beneficiaries the same year?

Generally no — if a family trust actually pays or makes payable a capital gain to a beneficiary in the same year it's realized, and makes the proper election, the trust can deduct that amount from its own income, so the gain is taxed in the beneficiary's hands instead of the trust's. Without that election and an actual payment or right to demand payment, the trust would otherwise be stuck paying tax on the gain itself, generally at the top marginal rate with no personal exemption, which is far less efficient than having it flow through to a beneficiary in a lower bracket.

Getting the timing and paperwork right matters: the amount has to be paid or made payable to the beneficiary within the same tax year the trust realized the gain, and the trust needs to file the appropriate designation with its T3 return so the CRA treats the gain as flowed out rather than retained. A trust that distributes cash informally without following this process can end up paying tax on the gain anyway, while the beneficiary receives the cash tax-free, the opposite of what the family intended.

Because this involves precise year-end timing and trust accounting, it should be handled by the trust's accountant, not decided informally by the trustees.