I found only one study that had studied childhood asthma rates in/around Dar es Salaam. The data was found in an article published in 2014. The study was done with high school students. In this study, they had chosen two sites: one in Ilala (close to the city centre, urban environment) and one in Bagamoyo (located about 1,5 hours from Dar es Salaam.
The overall asthma rate was: 11.8%. Comparison between the two sites revealed that pupils in Ilala district had a higher asthma rate (17.1%) than in Bagamoyo (6,6%)
There seem to be no studies done on a national level that measure the percentage of asthma in children. The only other studies I found online comparative study between Tanzania and Cameroon from 2004 (Source: https://www.ncbi.nlm.nih.gov/pubmed/15510944). The most recent study is from 2019 in a paper that assess under five mortality rates that name asthma as being a significant contributor (www.journalajpas.com/index.php/AJPAS/article/download/28788/54094/)