If by "wingsuit" you mean the sorts of suits used by BASE jumpers and high performance aerobatic skydivers to extend their range and manoeuvrability, then you have a problem with "steampunk" technology: low power to weight ratios.
Leonardo Da Vinci does not approve
Yes there are relatively high performance steam engines and even today the thermal energy plants using steam have all kinds of special equipment to wring the last bit of energy from coal, but generally speaking it requires a fair bit of size to effectively place superheaters, bottoming cycle expanders and so on, and much of the efficiency is a function of scale (tiny superheaters would probably end up being energy sinks, rather than ways to boost the output of your steam engine).
Then, of course, in addition to having large and bulky machinery strapped to the wingsuit, the pilot or jumper also is carrying a hot firebox to raise steam, a high pressure boiler or reservoir for the steam and an expander (steam engine) whirling away, all right next to the soft squishy human part of the equation, plus a lot of plumbing devoted to moving high and low pressure steam around. A steam leak or boiler failure isn't going to go well for the pilot.....
There is a barely plausible way to have steampunkery for your wingsuit, but it might be a bit alarming for the user: steam rockets.
The simplest version is what Bob Truax used to power Evel Knievel's rocket motorcycle for the jump over the Snake River Canyon. The rocket was essentially a pressure cooker vessel filled with high pressure live steam, which was then rapidly vented to generate the thrust needed to "jump" the canyon.
Skycycle X-2 steam rocket
Two other methods are possible, using exothermal reactions to generate steam, both pioneered by the Germans in the Second World War. The Me-163 rocket interceptor was powered by a rocket engine using decomposing hydrogen peroxide to generate steam and thrust. Two versions were developed, one using a Hydrogen Peroxide based monopropellant, and a more scalable and throttle able one using a bipropellant (Hydrogen Peroxide as the oxidizer and a methanol based fuel as the propellant).
Me-163 Rocket interceptor
HWK-109-509A rocket engine from a Me-163
The issue here is the fuels used (C-Stoff and Z-Stoff) are insanely dangerous, highly corrosive and safe handling requires thousands of litres of flowing water to wash away spills.
Only somewhat less dangerous was system devised by Hellmuth Walter to use H2O2 as an oxidizer for a hydrocarbon fuel like diesel. This is a combustion system which burns the diesel or other fuel in the oxygen released by the decomposing Z-Stoff, while also providing steam (which in many Walter designs was used in conjunction with the flame to power a turbine, most notably in submarines).
So by using either of these methods, the pilot can fuel the wingsuit (with suitable precautions) and use rocket power to take off, fly and even land. The overriding danger is if any of the oxidizer is destabilized prior to combustion, there will be a nasty explosion (probably on the user's back) and they will be doused with highly corrosive liquid or spray. The other issue of a hot rocket exhaust can be moderated with some clever engineering.
Gene Shoemaker with a Bell rocket belt, powered by decomposing Hydrogen Peroxide