No, "I have been knowing him since 2005" is not correct. You have to say here "I have known him since 2005".
However, you can use other "stative" verbs with the -ing form in many cases, but this is not one of them. Here are just a few examples of where you CAN use these verbs in this manner:
1. I have been HOPING to meet you for a long time.
2. I have been THINKING about this situation for months.
3. I have been FEELING sick since Thursday.
4. I have been LOVING this job ever since I started working here.
5. I have been HATING this job since John became my boss.
6. I have been BELIEVING his lies for too long.
7. I have been DOUBTING his lies for a long time.