(1) They do support LN according to their website. See my screenshot below. So one way to build this would be to get access to their permissioned api and make a web version.
(2) But it might be easier to go the permissionless route. Some of those apps support networks that lightning can do atomic swaps to. And some of them are very quick. So someone who doesn't mind getting their hands dirty by writing smart contracts on an altcoin platform could make this happen without needing to ask for an API credential from Flexa.
