Service blueprinting is a process analysis methodology proposed by Shostack (Shostack, 1982, 1984). Shostack’s methodical procedure draws upon time/motions method engineering, PERT/project programming and computer system and software design. The proposed blueprint allows for a quantitative description of critical service elements, such as time, logical sequences of actions and processes, also specifying both actions/events that happen in the time and place of the interaction (front office) and actions/events that are out of the line of visibility for the users, but are fundamental for the service. Service blueprinting involves the description of all the activities for designing and managing services, including schedule, project plans, detailed representations (such as Use cases) and design plans, or service platforms. 
Blueprinting is often supported by methodologies that elicit functional elements of services, as well as their qualitative/implicit characteristics 

On the other hand, A flowchart is common type of chart, that represents an algorithm or process, showing the steps as boxes of various kinds, and their order by connecting these with arrows. Flowcharts are used in designing or documenting a process or program in various fields. This makes them useful tools for communicating how processes work, and for clearly documenting how a particular job is done. Furthermore, the act of mapping a process out in flow chart format helps you clarify your understanding of the process, and helps you think about where the process can be improved. 

A flow chart can therefore be used to: 

Define and analyze processes; 
Build a step-by-step picture of the process for analysis, discussion, or communication; and 
Define, standardize or find areas for improvement in a process 
Also, by conveying the information or processes in a step-by-step flow, you can then concentrate more intently on each individual step, without feeling overwhelmed by the bigger picture.