It has nothing to do with cookies. That is just how dullta.com is. Sometimes you have to search by price. Sometimes by schedule. Sometimes one way. Sometimes multicity, to see the KE flights.

To put it all together and book it there is no way around it, you need to call DL and do it by phone. Check availability one way, segment by segment (as both price and schedules, sometimes one will work, sometimes the other, to show you availability) online, then call to book and give the flights one-by-one to the agent to put in.

If you ticket it as one ways, it may be very hard if not impossible for DL to combine the tickets into one and reticket (it normally can't be done), and also then your taxes/fees will be way messed up also.