The only Silverstripe related thing I can think of would be to ensure that the following is in your mysite/_config.php.
Beyond that, it's really an Apache/MAMP issue so you may have some luck in the MAMP forum if you can't solve it now.
I'd temporarily eliminate Silverstripe from the equation and confirm that mod_rewrite is enabled and functioning correctly.
I'm not sure exactly how MAMP Pro does it, but the Apache configuration for MAMP is in /Applications/MAMP/conf/apache. The main configuration file is httpd.conf. Remember to restart the web server to load in any config changes.
You need to confirm that there is a line like this in httpd.conf.
LoadModule rewrite_module modules/mod_rewrite.so
You could also run the following in the terminal
/Applications/MAMP/Library/bin/httpd -M | grep rewrite
This should return
From memory MAMP Pro has a slightly funky way of setting up virtual hosts. Perhaps you could create a new virtual host without silverstripe and check the most basic mod_rewrite test you can create.
Another tool in your toolbox would be to log mod_rewrites activity by adding the following to httpd.conf (and restarting server)
RewriteLogLevel 1 #(Could be higher but this should be enough for now)
Look through your apache logs in /Applications/MAMP/logs and see if there are any clues there.