Almost right! It should be 'I don't always speak English very well.'
Here's a tip about word order, which is especially useful for Spanish speakers -
Never put any extra words (such as adverbs) between the main verb and its object.
As you know, the basic English word order is SVO [subject] + [verb] + [object]. In the case of your sentence, the basic sentence is this:
[I] [don't speak] [English]
and the extra words are the adverbs 'always' and 'very well'.
You are right to put the word 'always' between the auxiliary verb ( don't) and the main verb ( speak). This is the normal position for an adverb of frequency.
However, unlike in other European languages, we don't normally separate the main verb ( in this case 'speak' ) from its object (English). The second adverb phrase, 'very well', needs to go at the end.
I hope that makes sense. Here's another little exercise you can do to check and reinforce this point:
Add the words 'usually' and 'in the evenings' to the sentence 'He doesn't drink whisky.'