Well, there is the Chaos Subjugation CB, which - like the Chaos Raid - increases Favour by one for each won war. Much more usefull for gaining favour is sacrificing to your gods, which gets you a lot more Favour (various amounts, up to 7 AFAIK) and various other boni (magic, traits, stat boost) but costs a lot in terms of both piety and money and is rather unreliable (you can offer the largest amount of money and still get nothing). If you're playing in the Chaos Wastes, there are also some random events that can give you Favour directly, but if you're playing in the Wastes, the game does everything to screw you over, so I guess thats rather unfeasable. Additionally, having a Daemon familiar can also give you random events which CAN give Favour (at least one of the event texts indicates it), but those events are a really unreliable way to get you Favour.
Ideally, you would use the Chaos Raid not to increas Favour directly, but as a mean to get the money and piety for the sacrifices.*
I don't think there is a way to check your Favour without cheats, but it actually doesn't matter. You can't really have ENOUGH Favour, because even if you pass the Favour threshold for champion/chosen/prince, having more than the required amount of Favour improves the chance of firing the (random) event that actually gives you the champion/chosen/prince trait. And given that these events have pretty high MTTH (up to twenty years for the Prince event) you definitly want to improve your chances.
Actually, to even attempt to become a Daemon Prince you should either have a very young and/or very healthy character to ensure a long reign, as it can take a very long time for the events to fire, it takes a very long time to acquire the Favour for even making the events possible to fire, it takes a long time to get all the piety/money to acquire enough Favour, etc. You do have time until your character is 100 years old (after that the events for champion/chosen/prince can't fire anymore), but even with a lot of health you're going to get traits like incapable/infirm/etc. that also prevents the events. So I'd say 65 years is the threshold after which you can pretty much forget about becoming a Prince. And I doubt that you can easily gain enough Favour before you're 50, at least. Also, you should probably have the congenital trait that allows you to become Prince (Strong for Khorne, Beautiful for Slaanesh, Genius for Tzeentch and No-Idea for Nurgle), as there is always a chance that you'll lose the lifestyle trait that makes the event possible.
*At last that's it for Khorne, which is arguably the most difficult god for aspiring Daemon Princes, due to the lack of free piety mechanics. There could be mechanics like the quirking or the Harem for Slaanesh, which could also give Favour, but I don't know about them.
Nurgle is the easiest you need to be sick to become chosen nurgle's rot is prefered
and kind , not greedy and sick tobecome a daemon prince