If you think about Huckleberry's feelings for his father while he is alive, we can certainly make a good assumption of what his feelings for his father are when he finds out that he is dead. When Huckleberry speaks of his father, he never does it under a good light.
Pap he hadn't been seen for more than a year, and that was comfortable for me; I didn't want to see him no more. He used to always whale me when he was sober and could get his hands on me; though I used to take to the woods most of the time when he was around.
What we can see from this statement is that Huckleberry Finn neither misses nor seems to love his father. After all, his father has not been there for him and, what's worse, his father is an abusive drunk. Huck thinks so lowly of his father (and with a good reason) that when he talks about him he uses a very detach point of view.
If I never learnt nothing else out of pap, I learnt that the best way to get along with his kind of people is to let them have their own way.
As if that weren't enough, Pap Finn is such a low life that he is even bitter that his son has at least been raised properly.
"Don't you give me none o' your lip," says he. "You've put on considerable many frills since I been away. I'll take you down a peg before I get done with you. You're educated, too, they say – can read and write. You think you're better'n your father, now, don't you, because he can't? I'LL take it out of you. Who told you you might meddle with such hifalut'n foolishness, hey? – who told you you could?"
Then, in the last chapter when Jim discloses to Huck how Pap's body is found dead from the flood, we see that Huck simply says nothing-absolutely nothing- at all, and wraps up his narrative explaining that Tom is "OK". Even with Jim's careful delivery of the news, we still get no reaction from Huck.
Doan' you 'member de house dat was float'n down de river, en dey wuz a man in dah, kivered up, en I went in en unkivered him and didn' let you come in? Well, den, you kin git yo' money when you wants it, kase dat wuz him.
This what Huck says after he hears the news.
Tom's most well now, and got his bullet around his neck on a watch-guard for a watch, and is always seeing what time it is, and so there ain't nothing more to write about, and I am rotten glad of it, because if I'd 'a' knowed what a trouble it was to make a book I wouldn't 'a' tackled it, and ain't a-going to no more. But I reckon I got to light out for the territory ahead of the rest, because Aunt Sally she's going to adopt me and sivilize me, and I can't stand it. I been there before.
Hence, we can safely conclude that Huck feels no joy nor pain for his father's death. After so many years of abuse and trying to get away from him, his death will certainly be quite welcome and also expected. Huck knows how sick his father is, and that the problems were caused by alcohol. If anything, Huck takes Pap's death as a very real part of his father's low and poor life.
Huck probably does not feel too bad that his father is dead. His dad was never much of a father figure, Jim acted like his father more even though they were not related. He does not seem happy nor angry when Jim tells him he found his dad dead, he just takes the news. If he was willing to fake his death to get away from him, he did not care very much for him given he was hostile and abusive.