My DS will be a year on the 27th as well, and he does the same thing with his sippy. He'll take a suck, maybe two, then just plays with it. I took the anti-leak stopper out months ago, but he's still not interested. We tried a straw one and he just chews on that too. He doesn't like holding his own bottle either, we can trick him into it sometimes if he's distracted, and he's starting to do it a little more, but I think he just likes being able to play while eating and being close/held by us. It can get frustrating but I generally just roll with it.
I feel like he's a bit behind in that area (compared to where others tell me they are anyway), as well as with eating solids (still not big on trying new finger foods or having variety)- I already know that there is no way he's going to be off the bottle by his birthday. We're working towards it, and I'm going to keep trying to get him to take his sippies, but I know that it might not happen. I'm going to try a more transitional cup type sippy because he tries to use his dipper toys to drink the bath water like a cup, so I'm thinking that might work better for my DS.
So, while I don't have any great advice other than to keep trying, I can definitely can relate! I'm right there with you. Good luck to you!