I know Five Card Draw isn't generally that popular but I play it occasionally and I've been wondering about this for a while.

Let's say I begin with the hand As-Ac-3s-8s-Js. I run into this dilemma constantly, and I never truly know what to do. A flush is a much stronger hand than a pair obviously, but when I have to call a big bet I only have around a 20% chance of getting that flush.

So I know that of course you could fold, but if, hypothetically, you couldn't, what do you discard here?

If you have JJ+ as your pair you should draw to the pair in most scenarios. It gets trickier when its like 55+ ace high flushdraw. Then it depends on the situation. AA+ flushdraw is auto AA IMO.

IMO description is not detailed enough.
But it's obvious, that if the "big bet" from this opponent means he has set+ than you'd better draw 1 to A-high flush (20%). You will have set+ only 12,5% drawing 3 to AA and still lose to straits and K-high and lower flushes catching AAA.

If you get 3 bet with a playable pair JJ+ I prefer to draw to the flush since a lot of times you are behind and possibly drawing as worse as needing to boat your pair up. Draw to the hand that will win.