I do feel they were genuinely friends. They might have started with the intention to take each others help gain their personal goal, however later they genuinely grew very fond of each other
By the time of Mahabharata war, Karna had lost many at times to Arjun and once to Bheem. There was no reason for Duryodhan to believe that he could be a match for Arjun, nor was he a good strategist (I don't think he ever gave any beneficial idea to Duryodhan) yet he never ignored him and kept him in his innermost circle where even his own brothers (excluding Dusshashan) didn't have the entry to. Aside he agreed when Bheeshm said Karna would not be a part of his army. Duryodhan had many at times rejected the orders of Bheeshm and it was no way difficult for him to do the same this time as well, but he decided otherwise. Had Karna only been an important weapon for Duryodhan, he would have either removed Karna from his close circle or would have insisted Bheeshm on having Karna fight. But he did neither. This shows his genuine bond for Karna
Karna on the other hand did always remain loyal to Duryodhan (at least before his promise to Kunti), didn't hesitate to use his Indrast on Ghatochkat when Duryodhan asked him to do so despite him knowing that without that defeating Arjun was difficult (he would have never agreed for this had his only aim been defeating Arjun) supported Duryodhan in Lakshagriha, although the death of Arjun would have meant Karna never being able to defeat Arjun just because that made Duryodhan happy.
They were similar in thoughts and resonated with each other. That's the only quality which makes two people friends and they did possess it
Contrary to what we believe people in Mahabharata were grey (not only the supposed good characters but also the bad characters, just the percentage of good n bad qualities varied) Duryodhan and Karna had many vices but they did have their own set of good qualities too, their friendship definitely was one such example
Edited by FlauntPessimism - 5 years ago