A (good) friend of mine wants to gift me miles through his credit card program that can transfer miles to a variety of frequent flyer programs without fees. My goal is to ultimately get from Chicago to Phuket in Business or First. But it looks like it may be better to fly to Bankok or Singapore instead and get a local flight the rest of the way (fewer points, more flight options, etc, plus a free layover).

Delta is my primary rewards program. The business-class flights there seem to cost 175,000 to 205,000 points (plus $250-$500) round-trip. A benefit of using Delta is that if the flight gets canceled I get the points back into an account I can actually use. I also consider the risk of them going bankrupt and both canceling my flights and making my points worthless is low.

Should I consider having my friend transfer into another airline instead? Are there airlines where this would cost much fewer points? Would it be suspicious if I open a new FF account, transfer in a bunch of points, and then book a flight with all of them? I have read that you can get your miles disqualified if you purchase miles (not what I'm doing but it could look like that).

I don't know the details of this credit card program - for one thing, you didn't say which credit card program it is, and they differ - but in most such situations, it's better for the owner of the miles to buy a ticket for the traveler than it is to move the miles into the traveler's account. That might mean your friend would have to be involved in what happens if the flight is cancelled, but if this is a good friend, that would presumably be okay with him/her.

It is some sort of American Express program. I don't think he can buy directly, so he has to either transfer miles into his Delta account and buy my ticket, or transfer the miles into my Delta account and I can buy my ticket.

it seemed the latter would be easier on him since he wouldn't have to be involved in the actual flight selection, notifications of flight changes, etc. But if that's not the case I'd like to know the details.

To be able to transfer the miles into your DL account you have to be an AU on his account for 90 days.

Yes ~ maybe. Some frequent flyer programs take a very dim view of a newbie transferring in cc points and then making long haul (premium cabin) award flights. If the cc points come in from a different credit card account-name to the ff account~name that may be other big red flags. That may not even be possible.

As above, better if you become an Amex AU or your friend gets the award for you from his ff account.
Note that selling-buying ff miles/cc points for cash is against the the t&c's of all ffp & cc loyalty programs I am aware of.
I notice you are using the word "buy" for an award flight. Awards are not bought

Airlines/aircraft/routes with first class is decreasing. And after COVID-19 ends will be even less than 2019.

As Yoshi212 says, I don't think that you can transfer Membership Rewards points into a DL account with a different name than the cardholder, unless that person is also an authorized user on the American Express card. And yes, there are many reports of people opening new accounts, loading them up with miles from aa credit card, buying a premium ticket, and then having the account closed and the ticket cancelled. I would not go that route. Just have him buy the ticket for you.

Don't use Delta they suck especially for South East Asia.

Amex MR will transfer to any Singapore Airlines KrisFlyer account no matter what the actual name on the account is. Has always been this way, I have 4 SIA accounts saved under my Amex MR and regularly transfer my points to these accounts in order to top them up.