In writing the Robert E Lee at War series (which begins to be released later this year) over the course of the last decade, I provide significant and detailed analysis of subordinates and their performances/development under Lee. With that in mind, please allow me to give a short answer to your question. And in keeping within the parameters of your question, I am addressing Jackson's tactical abilities---because his understanding of operational-level warfare was generally excellent, and second only to Lee's.
Therefore, regarding Jackson's tactical abilities, well, they cannot, under any realistic and reasonable measure known, be considered anything better than barely mediocre---at very best. At worst, he was very, very challenged in the realm of tactical handling of troops. He had many opportunities to improve, and never demonstrated growth in this regard. In essence, his lack of tactical expertise came up time and again. His tactical poor performances included, but were not limited to, Kernstown, Gaines' Mill, White Oak Swamp, Cedar Mountain, Groveton, Second Manassas, Sharpsburg, and, yes, Chancellorsville. Sometimes, the tenacity of the troops and leadership of subordinate commanders overcame Jackson's shortcomings---both on the offensive and defensive---were many times paid with a steep price. So, bottom line, is that while Jackson grasped the operational-level of warfare extremely well, his shortcomings in the tactical realm were on the other end of the spectrum. All these issues are dealt with in detail in the Robert E. Lee at War series.
You mention Jackson's flank attack at Chancellorsville. Ok, let's very quickly contrast that to Longstreet's at Second Manassas. Jackson deployed his divisions in brigades abreast, meanaing all the brigades of a division in a single line, perhaps three-quarters to a mile long... one line of divisions behind another, very similar to Beauregard's tactical deployment mess at Shiloh. This specific, poor tactical deployment, known in the military parlance of the time as "colonne de division par batallion,"robbed the division commanders of the opportunity to support their own line, makes a sustained, coordinated advance very, very difficult, and is absolutely counter to sound tactical deployments of the 19th century, as proven many times on European battlefields---and demonstrated again many times in the American Civil War by James Longstreet in his attacks.
In contrast, and from a purely tactical standpoint, Longstreet totally 'got it.' His attacks, formed in depth whereby divisions are deployed in multiple lines so that the rear brigade/line(s) can be brought up to support the front brigade/line(s), allows the division commander the flexibility needed to meet and answer most developing tactical situations. In the military parlance of the time, this was known as "colonne de bataillon par division." (Yes, these guys used the French terminology, and Lee frequently expressed his battlefield objectives using Napoleonic phraseology.) Longstreet demonstrated this understanding/expertise to launch his attacks in proper, supporting formations with his excellent/superb attack-in-depth deployments at Frayser's Farm, Second Manassas and Chickamauga. Thus, Longstreet's attack at Second Manassas, formed correctly using his divisions and in-depth, was able to sustain a drive deep into Pope's rear areas, despite the constantly growing number of Federals thrown in his path. Undoubtedly, Longstreet's would have succeeded in cutting off most of the Federal army from its retreat route if---if---Jackson had promptly obeyed Lee's two direct orders to advance in support of Longstreet's steamroller.