If you get complete combustion of any hydrocarbon fuel, your products will be primarily $CO_2$ and $H_2O$. Other products will be present in quantities too small to be relevant to the heat losses that you're looking at.
These two gases will change the heat capacity, conductivity and density of the flame and your exhaust gases. So heat heat transfer computations that you perform regarding convection and conduction should change accordingly. Note that these properties vary with temperature over the range that you're interested in (300–2,000 K, roughly), so it's best not to just pick one value.
The total energy from the fuel should be computed from the heat of combustion ($\Delta H_C$) of the gas being burnt. From balancing the chemical equations you can determine the amount of water produced for every mole of fuel. The heat stored in the water depends on it's temperature (look this up in a table or compute the integral of $c_p$ plus the heat of vaporization). The ratio $H_{H_2O}/\Delta H_c$ tells you how much energy went into the water.
These gases do thermally radiate as well and you may want to consider their emissivity, although the flame sheet itself (where combustion is still in process) is likely to be a more significant radiator.
The HHV-LHV difference is meaningful if you are trying to extract as much heat as possible from your exhaust gases. For example, after a turbine engine has extracted work from the combustion products, they'll be too cold to produce mechanical work, but could be used to heat a building. It just has to be cold enough for the water to condense so that the heat of vaporization can be released ( <100 °C).
You should be able to find most of the relevant thermal properties online (in the NIST Chem Web Book in the entries for 'fluid properties.' Any standard text of combustion (Law, Turns, Glass etc.) will usually have tabulated info (based on your project you should already have consulted at least one of those heavily).
