To second Robin's comments, make yourself familiar with the phonetics of Tagalog. The old abakada will help you get a feel for that, as will some of Mikey Bustos' videos on YouTube.

If you want to learn our accent, i think a better way of learning it is by starting to learn our phonetics. There are lots of sounds in English that are not in our language. So, it's a good idea to know what syllables are included in Filipino that are also found in English and those that are in Filipino but not in English or the other way around. In that way, you would be able to avoid unnecessary sounds that foreigners usually mistakenly say when speaking Filipino . If you are interested to know more about our language, just send me a message. :) I am willing to help.

I found Tongue position essential. In my native english, my tongue rests, withdrawn on the bottom of my mouth. In Filipino, i find i need to have my tongue pancaked, and standing proud, resting on my lower teeth. This makes it ready to flipped R's but just generally i found it easier to slip into the accent. When I went there, I often noticed that you could see the tip of a persons tongue as they listened / waited. I try to make most sounds from this resting position, the accent comes much easier then.