1) Can a person who reads Braille visually be dyslexic?
2) Can a person who reads Braille by touch be dyslexic?
3) Can a person who is written-language dyslexic also be dyslexic in Braille?
4) Will a person who is written-language dyslexic necessarily be dyslexic in Braille?
The answer to questions 1-3 is an unqualified yes. The answer to 4 is extremely complicated.
Dyslexia is a processing disorder and has, in theory, nothing to do with vision. A dyslexic reader does not "see" words incorrectly. The eyes correctly capture the information, but somewhere in the brain the information is "decoded" (or recoded) improperly, resulting in inaccurate phonological signals.
The stereotypical backwards letters or misordered letters (a symptom that actually occurs in only a very small percentage of dyslexics) is a symptom of incorrect language decoding, not visual decoding. In fact, dyslexia may be more commonly associated with auditory processing issues than visual ones.
This means that a person can in fact be "Braille dyslexic". The same coding and decoding difficulties that impede reading in English could impede coding and decoding of language in Braille.
This applies regardless of whether the Braille is processed visually or by touch. Once the brain is trained to recognize a symbol as language, whether that language is the Latin alphabet, Japanese logograms, or Braille patterns, there is a potential for improper coding and decoding.
Some people even experience dyslexia issues with fingerspelling in sign language. On the other hand, non-linguistic signals are unaffected, so a dyslexic person is unlikely to have difficulty recognizing pictures of things and properly identifying them. (Because dyslexia is often an underlying cause of, or accompanied by, aphasia and other speech disorders, it can create the impression of a visual disorder where there is none.)
Here is where it gets complicated; because there is no identifiable "language centre" of the brain, language processes are distributed across different sections of the brain. It is unclear exactly "where" and how the processing issues associated with dyslexia arise.
What we do know, is that dyslexia is not an "across the board" disorder,difficulty with one language does not imply difficulty with all languages. Orthographically "deep" languages, which have complex and varied relationships between letters and phonemes, such as English, pose different problems from those in orthographically "shallow" languages, which have more straightforward and consistent relationships between letters and phonemes, such as German, which are in turn different from logograms, where images, or graphemes, are not related to phonemes.
Dyslexia can occur in any, or all, or any combination, but difficulty in one does not necessarily imply difficulty in all. A language that takes advantage of a different "pathway" might "route around" the processing disorder, or it might be affected by it to a different, greater or lesser degree.
Braille, however, is not a "different language". Braille is a different script, but basic "uncontracted Braille" is a transliteration of the written language (let's assume for the moment we are talking about English).
In Braille, the pattern for a corresponds to the letter a, the pattern for b corresponds to the letter b, etc. Since dyslexia is not a visual disorder but rather a disorder in the coding / decoding of the linguistic patterns themselves, it is highly likely that the same linguistic difficulties would be encountered. That is, inputting the same letters by a different sense is unlikely to "route around" the coding malfunction.
Contracted Braille
That would be too easy an answer, though, so here's another wrinkle: most Braille texts are not printed in "uncontracted Braille". Because Braille is not nearly as compact as the written Latin alphabet, most Braille uses a set of contractions, substituting letters and letter combinations for words and letter combinations.
Contracted Braille has single-character contractions for letter combinations such as "sh" and "ch" and even some words such as "and" and "but". Additionally, longer words are frequently significantly contracted, such as "ll" for the word "little" and "xs" for "itself". So even though English Braille is in fact the English language, many words are spelled differently in printed Braille.
There are three "grades" of Braille spelling: Grade 1, uncontracted (a direct transliteration of English spelling); Grade 2, contracted (a large number of contracted spellings); and Grade 3, shorthand (an extremely contracted version used as shorthand, much like journalistic shorthand).
It is unlikely that contracted Braille would "route around" all of a dyslexic's processing problems. It could, however, mitigate some of them or it could actually exacerbate them by adding even more orthographic depth. In addition, because dyslexics often develop coping mechanisms to mitigate their own processing problems, learning Braille might pose difficulties related to a dyslexic's secondary functions, not the actual coding and decoding itself.
So here is the part where your particular question is important. If you just need to know whether a character could be dyslexic in Braille because you want to write a dyslexic Braille reader into your story, the answer is definitely, Yes.
If your character normally reads standard written English and is learning to read Braille, and you want to know how the dyslexia would translate over, it's not really clear.
It could mitigate the condition; if your character is only mildly dyslexic, this could be a huge advantage, although for anything other than only borderline dyslexia it is unlikely to mitigate it entirely.
Or the dyslexia could be just as bad, or even worse, in the new writing system. On the other hand, the process of learning to read Braille could provide the dyslexic character with some new coping strategies that allow him to function at a higher level.