While apparently rather simple at first sight, the word interaction is very often mispronounced. In fact, there are two pitfalls. First, as discussed in this recent post, action is pronounced as [ˈækʃn] rather than [ˈæktʃn], listen here. Second, a remarkable number of people do not pronounce the letter r in interaction, which is incorrect. The correct pronunciation is [ˌɪntərˈækʃn], listen here, with the t often flapped in American English. However, both the British and the American pronunciation have a clearly audible r. My personal theory is that the missing r is a result of an (incorrect) association with the pronunciation of words such as international or internal. In the latter, the r is not pronounced when speaking in a British accent (but is pronounced in American English; the incorrect pronunciation of interaction is also used by people who try to speak in an American accent). In the case of interaction, the pronunciation of the letter r is identical in British and American English.
More generally, in British English, the pronunciation of r for a given word depends on the context. For example, in the phrase
there is pronounced as [ðeər], because it is followed by a word starting with a vowel sound. In contrast, in the phrase
there is pronounced as [ðeə], that is, without the r. The reason is that, similar to interaction, “there is” is easier to say if the r is included. Another example is the pair of phrases
Is there more tea? (there pronounced a [ðeə])
Is there any tea? (there pronounced as [ðeər]).
Finally, once you have mastered the basic pronunciation of interaction, make sure you also stress the correct part of the word, see here.