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Knowledge graphs (KGs), with their flexible encoding of heterogeneous data, have been increasingly used in a variety of applications. At the same time, domain data are routinely stored in formats such as spreadsheets, text, or figures. Storing such data in KGs can open the door to more complex types of analytics, which might not be supported by the data sources taken in isolation. Giving domain experts the option to use a predefined automated workflow for integrating heterogeneous data from multiple sources into a single unified KG could significantly alleviate their data-integration time and resource burden, while potentially resulting in higher-quality KG data capable of enabling meaningful rule mining and machine learning.In this paper we introduce a domain-agnostic workflow called BUILD-KG for integrating heterogeneous scientific and experimental data from multiple sources into a single unified KG potentially enabling richer analytics. BUILD-KG is broadly applicable, accepting input data in popular structured and unstructured formats. BUILD-KG is also designed to be carried out with end users as humans-in-the-loop, which makes it domain aware. We present the workflow, report on our experiences with applying it to scientific and experimental data in the materials science domain, and provide suggestions for involving domain scientists in BUILD-KG as humans-in-the-loop.