I am a non native speaker from Europe (my native language is Slovenian) and I'm trying to improve my English accent and pronunciation but I'm struggling with the flap t sound. I can pronounce it in most words that don't have an r sound or r colored vowel in them. However when I pronounce words like better or water it starts to sound like two consecutive r sounds or a strong d and an r sound. Is there any specific way to practice this or have I just not practiced enough?
Your description of the problem suggests to me that you're syllabifying the wrong way. Am. English syllabifies bett-er, wat-er. The middle consonant goes in the first syllable, not the second. And since sounds in different syllables are less likely to affect one another, the middle t (once it is flapped) is more susceptible to being affected by the preceding vowel, which is in its own syllable, than it is to being affected by the following vowel, which is in a different syllable.
If you put the middle flap from t into the wrong syllable (which is the second syllable), be-tter, wa-ter, it is more likely to be affected by the second vowel, which is a syllabic r. And it sounds to me like that is what is happening in your speech. The flap from the t is getting retroflexed because of the following r. If you can get the flap into the first syllable, maybe that won't happen.
Unfortunately, I can't think of a good way of explaining how to say bett-er, with the right syllabification, at a normal rate of speech, so that the t flaps. Trying to sound out the word, syllable by syllable, doesn't work, because then the t won't be flapped and will be in the second syllable -- be-tter -- which is not what you want. Like other consonants at the end of a syllable, t between vowels at the end of a syllable is a weakly articulated sound. In fact, that's why it changes to a flap. So, it may help to articulate the flap with less energy, to get it into the previous syllable and preventing it from assimilating to the r.