Server A:
ip 1.1.1.5
gw 1.1.1.254

Server B:
ip 1.2.2.5
gw 1.2.2.254

First of all, is it even possible to route via another server? Assuming nothing tricky is being done in the datacenter (which I know there is but we don't know what so forget about that for now), it would be server a -> switch -> server b (possibly router in between depending on locations of the server).

If so, is it possible to get a little more granular, such that some traffic/ports go via one server, others via another, even possibly in a different datacenter altogether?

And from the other perspective, can applications (TCP/UDP mainly) deal with this type of routing?

What about if it via multiple load-balanced places?

I know general networking stuff, ccna level, but I haven't read of anyone doing this so I'm not sure if there is any GOTCHA that I've not thought of.

what do you actually want to do?? It feels like there's a big paragraph missing at the start that explains what you mean by "routing via another server" Do you mean something like application load balancing? Somethign nginx is a reasonable starting point for if its web traffic.

Yea there is a big paragraph missing because I am not sure how much I want to say, >_>

Basically, there are restrictions on the limit/amount/speed of traffic from server A to the internet, but not from server B to the internet. So we want to take outgoing traffic from server A, route it via server B, onto the internet. Then incoming can go normally to server A.

are your both server same location ? same swicth ? If this, Both server having a A class IP , Please check both able to ping each other.

There are certainly ways to achieve this, but depends on your network, and also things like the type of traffic and the mission criticality of the solution. what type of traffic is it? Who is initiating it? I'm a little concerned that you are wanting a remote browser to connect to A directly but then drugstore get all data back via B, and at a tcp/ip level that's not possible.

Same datacenter yes, different switch different subnets.

It isn't browser based, it is application level (which uses TCP/UDP). It would be fairly symetric traffic. There is no SLA required, so it doesn't so much matter if data is lost as long as not too much is lost.

Would it help to have a diagram or something?