|another user on a Macbook is also connected to the wireless router and never has these issues, leading me to believe it's my computer. |
This would be my first suspicion too. I'm guessing when you flush the DNS cache, you're doing it on the problem Mac and not on the router. If this is correct then this almost certainly points to the computer.
You can give guapo's suggestion a try and put the ISP's DNS addresses in manually on your Mac and see if that doesn't fix the issue. If it does, great, if it doesn't, then I can't really be of any help to you, I'm not a Mac guy.
The only thing I can suggest is seeing if there are updated drivers for the network interface on that Mac and if there are, update it. If not, you may be having issues with either the TCP/IP protocol stack, or the device itself may be having hardware issues. In any case, you'd need to find a Mac tech to get to help you. Sorry.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.