If I understand correctly, your computer serves as a Wifi Access Point, so it should have a dhcp server running on wlan0, is that so ?
Assuming this is the case, First you need to have /proc/sys/net/ipv4/ip_forward set to 1 instead of 0 (if you are using IPv4, I don't know the equivalent for IPv6, if there is any)
The iptables command you are looking for is
iptables -t nat -A POSTROUTING -o eth1 -j MASQUERADE
iptables -t nat -A POSTROUTING -o eth1 -j SNAT --to-destination <eth1 IPv4 address>
This will masquerade all IP addresses from wifi to one eth1 has and magically redirecting all response packets to the correct device on the wifi network
To use Burp, the simplest thing to do is to configure Burp as a proxy on the wifi devices. If not possible, You need to set two listeners with "Invisible Proxy support" for Burp, one for HTTP (let's say on port 8080) and one for HTTPS (let's say on port 8443). Then the iptables commands will be :
iptables -t nat -A PREROUTING -i wlan0 -p tcp --dport 80 -j REDIRECT --to-ports 8080
iptables -t nat -A PREROUTING -i wlan0 -p tcp --dport 443 -j REDIECT --to-ports 8443
If I remember correctly, that should do the trick.