Have you correctly configured the Subnet Mask for BOOTP/DHCP Server?
Go to Tools>Network Settings
Do you have a wireless network connection on this computer and if so is it disabled?
If your LAN connection is set to "Public" then try setting it to "Home" or "Work".
There a few reasons why the adapter's Module Status LED may be flashing Red, but as you are only at the IP address setting stage, it is most likely that it is just not configured correctly yet. I would get the static IP address assigned first and then tackle the Module Status.
From your screenshot, BOOTP/DHCP Server appears to be successfully assigning the adapter a DHCP (Dynamic) IP address, which you now need to set Static.
If you cannot disable BOOTP/DHCP via BOOTP Server, then you can also attempt to do so in RSLinx Classic using the currently assigned DHCP IP address. If you can browse to the adapter using and Ethernet driver, then you can right-click it and go to Module Configuration>Port Configuration and set it to Static.
You can also do the same as above in RSLogix 5000/Logix Designer under the I/O Configuration, if the adapter has been added.
If the DHCP IP address is not being successfully assigned by BOOTP/DHCP Server, then you would have to initially set the adapter to a known IP address (192.168.1.x) using the thumbwheel, and also assign your computer a unique IP address on the same Subnet (192.168.1.y), and then use RSLinx Classic or RSLogix 5000/Logix Designer.
Another option, once a known IP address has been assigned via the thumbwheel, is to use an Internet Browser to browse to the adapter's embedded HTML webpage. Here you can go to Configuration folder on the left and expand it [+].
Then go to Network and from here you can disable BOOTP/DHCP and assign your Static IP address.
Click Apply Changes
Hopefully something there will get you going.
P.s. If you do assign an IP address via the thumbwheel, don't forget to set it back to an invalid number when done (255 through 887, or 889 through 999).