I have never configured a mikrotik router to do this, but i do have a similar setup and i think its not a gear depandant issue. If i understand you correctly, there are a couple of ways you can do it:
OPTION 1
route all the vlans on your layer 3 switch so that all internet traffic goes through a single vlan then connect that vlan (UNTAGGED) to the mikrotik router. using a configuration like this does NOT require a VLAN TRUNK to the router, as all traffic is ROUTED across another vlan.
given your diagram, consider this:
VLAN1 has the subnet 192.168.1.0/24, give the switch an IP address on this VLAN of 192.168.1.2
VLAN2 has the subnet 192.168.2.0/24, give the switch an IP address on this VLAN of 192.168.2.2
create VLAN3 with 192.168.0.0/24, give the switch an IP address on this VLAN of 192.168.0.2
give mikrotik an inside IP of 192.168.0.1, and connect this interface to an UNTAGGED port on VLAN3.
create static routes on layer 3 switch:
0.0.0.0/0 > 192.168.0.1 (default route points to the mikrotik inside IP)
192.168.0.0/24 > 192.168.0.2
192.168.1.0/24 > 192.168.1.2
192.168.2.0/24 > 192.168.2.2
you also need a route on your mikrotik to route ALL 192.168.0.0 traffic back to your layer3 switch:
192.168.0.0/16 > 192.168.0.2 (using a 16bit mask will allow you to add more vlans in the 192.168.x.x range later without having to tweak the route)
my example uses static routes to let you see whats going on, but you could also set up RIP.
keep in mind, with this setup you may need to create some access-lists, or routing rules (whatever your vendor calls it) to keep traffic on VLAN1 from being routed to VLAN2, if you need the vlans completely seperate.
OPTION 2
do no routing on your layer 3 switch (then you wouldnt be using layer 3 on the switch!)
trunk all vlans (add all vlans as TAGGED) to 1 port on your layer 3 switch and plug that in to your mikrotik. create all the vlans on your mikrotik inside interface as TAGGED, add the proper IPs to each vlan interface (see above). then let your mikrotik handle all the routing and firewalling between vlans and internet.
i dont think this is the best option, as typically your internal LAN runs at a higher speed than you can put through your router, and this shifts the burden of all internal routing to your router away from your layer3 switch… i only mention it because it can be done this way and may be better for a small network because of simplicity.
as i said, ive never done it with mikrotik, but ive done it with several other vendors, its just routing and vlanning 
hope that helps!