No, I think your first bet on the flop was good. I would call the raise to 14,000 but I would be concerned that I was losing to JT. I would expect that my flush draw might be good if it hits, or I could be ahead to the nut flush draw. With the paired board on the turn, I would be wary that I was beaten by a full house.
I don’t expect to need the nuts to win because I almost always raise preflop. That means I play fewer multi-way pots.
In a flop against 6 opponents, I do want to have the nuts before playing a big pot because there is a good chance somebody flopped the nuts. It is fine to bet your big hand/draw, but be wary. When you re-raise, what hands will give action? JT/65 or possibly the nut flush draw or combo draws that have good equity.
It is possible that they could be raising with two pair or a set, but given the number of opponents and the size of your bet, it makes more sense that they have a straight. It looks like they are trying to get value rather than folds. My overall point is not to play afraid, but that 2nd best hands need to be played carefully in multi-way pots (and it’s best to avoid multi-way pots when possible).
Min-raising in general looks very strong because while they could be trying to protect a draw, they could see the draw for cheaper by just calling. Usually a min-raise means they don’t want you to fold because they are extremely strong.