scoring flush and run

Just come back to cribbage after many years and have been playing online for practice. Site scores for me and, very unusually, the hand had a flush and a run but the scoring only scored for the run; is there a rule somewhere about this, please? Also, I am seeing different rules for runs and flushes, e.g. some must include the starter card and be 5, others say you can count the 4 in your hand and others say that in the crib is can only be 5 although 4 allowed in hand. Bit confused. Thanks.

Runs and Flushes

These are covered very clearly on this site and on cribbage.org. You score one point for each card in a run of sequential cards, but you can only use the same exact cards once. Flushes are only if all 4 cards in your hand (can be 5 with the starter card) are the same suit, score one point each card. For a flush in the crib, all 4 cards in the crib AND the starter card must be the same suit. Score one point each card (5 for the flush in the crib)

scoring runs during play

is it possible to score a double run while pegging? 3-2-5-4-3-5 for eg?
I have played and people are taking double runs during play and I am saying no, is this correct?

Right You Are

You are correct. There is no such thing as a double run in pegging.