You can earn Krisflyer status miles on Alaska, JetBlue and United, find the earning chart here: KFOALLevels.pdf

However, the only domestic airline where SQ KF status will net you benefits is United. Especially with Gold status gained through Krisflyer, you will get lounge access on all domestic trips on United - this saves you from having to buy a lounge membership ($650 annual fee, or $525 annual fee for the co-branded credit card that includes lounge access). Also, as only United is a member of Star alliance, airport benefits (priority check-in, extra baggage allowance...) apply only on United, not on the other partner airlines.
You can maximize FF benefits flying on SQ by either switching your domestic flying to United and crediting your SQ flights to United's program (this will get you more domestic upgrades and allow for more mile-earning opportunities via non-flying activities like using co-branded credit cards etc) or by switching your domestic flying to United and crediting all flights to KF - this will give you better treatment on SQ as well as Star Alliance gold benefits on UA (namely, lounge access on domestic itineraries, something you don't get with UA status) once you have attained Gold status on KF..
Pitfalls: Most Economy fares on SQ do not earn anything in United's program. If you fly 'cheapest possible' and end up with G, I, K, N, O, Q, V, X fares, you have to credit them to KrisFlyer if you want to earn miles with them. See https://www.united.com/ual/en/us/fly...-airlines.html.
Even with KrisFlyer, discount economy tickets don't earn much; you'll have to fly six USA-SIN returns per year to qualify for Gold. Silver status is practically meaningless on any other airline except SQ.

If you don't fly enough to attain Gold status in Krisflyer (use the calculator on SQs website) and keep doing this for at least a few years (remember that KrisFlyer miles expire after three years, so you'll have to get enough for an award/upgrade before that date) , I`d keep flying Delta if you are happy there. If you are buying the tickets yourself and you won't mind a connection, fly to Singapore on Korean via ICN and earn miles on Delta instead of taking SQ.


edit: After reading the other thread where you say you'll be flying Premium Economy/business class and your final destination is DVO - well, it looks like you'll get to Gold pretty quickly by just flying this route .
Credit these flights to KrisFlyer and leave everything as is with Delta - this way, you get status on SQ/ in Star Alliance in addition to what you already have. Or - as when flying business class you don't really need status - credit them to Alaska's program, as that will give you the best redemption options and the most flexibility as they don't expire.

Besides SQ, the nicest option to get to DVO is with Qatar via Doha. This should be price-competitive with SQ, have you a lie-flat seat all the way, and you can credit the flights to Alaska as well.

Personally, I would not want to fly on the JFK-SIN nonstop in anything but a business-class seat. That flight takes eighteen-and-a-half hours - just too long to not have a bed. Also, if you buy PE, you'll be sitting in economy with just 30" seat pitch for almost four hours on the SIN-DVO leg.
And even the business class seats on these flights draw a lot of criticism - see media coverage (read the comments on that one as well) or the threads on here
If I were paying for the tickets myself or would be subjected to a "cheapest PE" corporate policy , I`d:
- credit all flights to KrisFlyer
- fly the route via FRA and use the layover to stretch my legs, avoiding the 18-hour nonstop.
- use the miles for upgrade awards to upgrade to business class on that route whenever possible, especially if you have to take the ULH nonstop.

This may sound like first-world problems, but having to sit in an airplane seat for 40 hours each time you go there and back gets very tiresome very quickly.